
715 N.W.2d 512 (2006)
271 Neb. 659
Carl and Linda HAMIT, appellees,
v.
Tanya HAMIT, appellant.
No. S-05-245.
Supreme Court of Nebraska.
June 2, 2006.
*517 James C. Bocott, of McCarthy, Moore & Hall, North Platte, for appellant.
Michael E. Piccolo, of Dawson & Piccolo, P.C., L.L.O., North Platte, for appellees.
HENDRY, C.J., CONNOLLY, GERRARD, STEPHAN, McCORMACK, and MILLER-LERMAN, JJ., and HANNON, Judge, Retired.
MILLER-LERMAN, J.

I. NATURE OF CASE
Tanya Hamit, appellant and the mother of Wyatt and Garrett Hamit, appeals from the order of the district court for Lincoln County, which concluded that Nebraska's grandparent visitation statutes, Neb.Rev. Stat. §§ 43-1801 to 43-1803 (Reissue 2004), were not unconstitutional and awarded grandparent visitation to the children's paternal grandparents, Carl and Linda Hamit, appellees. In this appeal, we are called on to determine, in light of the U.S. Supreme Court's decision in Troxel v. Granville, 530 U.S. 57, 120 S.Ct. 2054, 147 L.Ed.2d 49 (2000), whether Nebraska's grandparent visitation statutes are unconstitutional. We conclude that Nebraska's grandparent visitation statutes are not unconstitutional as applied to appellant, and we further conclude that the district court did not abuse its discretion in awarding grandparent visitation to appellees. We affirm.

II. STATEMENT OF FACTS
Appellant married Jeremy Hamit (Jeremy) in October 1999. Appellant and Jeremy had two children, Wyatt, born on September 7, 2000, and Garrett, born on December 30, 2002.
Appellees are the parents of Jeremy. Appellees own and operate Wallace Flying Service, in Wallace, Nebraska. Jeremy and appellant worked for the flying service during their marriage. Jeremy was a pilot, and appellant was an office assistant. Their children, Wyatt and later Garrett, would accompany Jeremy and appellant to work and would be cared for by appellees when Jeremy and appellant were occupied. The grandchildren were also frequent visitors to appellees' home.
Following Garrett's birth, appellant filed for divorce from Jeremy. During the pendency of the divorce proceedings, Jeremy had custody of Wyatt and Garrett every other week. When Jeremy had custody, he would regularly bring the children to visit appellees, and appellees were actively involved in the care and nurturing of their grandchildren.
On April 4, 2004, prior to the divorce trial, Jeremy died in a plane crash. Following the death of Jeremy, appellees contacted appellant in an effort to continue visiting with their grandchildren. After an initial visit between appellees and the grandchildren, however, appellant did not respond to appellees' further attempts to schedule visitation.
On May 4, 2004, appellees filed their petition in the district court for Lincoln County seeking grandparent visitation pursuant to Nebraska's grandparent visitation statutes, §§ 43-1801 to 43-1803. Appellant opposed appellees' petition. During the pendency of the visitation proceedings, the district court awarded appellees temporary visitation with Wyatt and Garrett every other Saturday.
*518 In appellant's amended answer, she challenged the constitutionality of Nebraska's grandparent visitation statutes. In the district court and on appeal, appellant claims that given the fundamental nature of her parental rights, the Nebraska grandparent visitation statutes violate her substantive due process rights guaranteed by the U.S. and Nebraska Constitutions.
On December 7, 2004, appellees' petition for visitation came on for trial. A total of 11 witnesses testified, and several exhibits were admitted into evidence. On January 7, 2005, the district court entered its order. The order is eight pages in length. The order recites numerous findings of fact and, in some cases, determines the credibility of witnesses. In its order, the district court concluded that Nebraska's grandparent visitation statutes were constitutional. The district court further determined that the evidence presented at trial "was overwhelming and established beyond any doubt, and certainly by clear and convincing evidence that each of the factors set forth in the Nebraska grandparent visitation statutes have been proven by [appellees]." The district court ordered the parties to comply with a specific visitation schedule, which granted appellees visitation with their grandchildren on the first Saturday of each month, from 9 a.m. to 7 p.m., and for 7 consecutive days in the summer. Appellant filed this appeal from the district court's order.
Additional facts will be set forth below where pertinent to our analysis.

III. ASSIGNMENTS OF ERROR
On appeal, appellant assigns several errors. Appellant claims, renumbered and restated, that the district court erred (1) in concluding that Nebraska's grandparent visitation statutes were constitutional on their face and as applied to appellant and did not violate the due process provisions of the U.S. and Nebraska Constitutions; (2) in determining that appellees had attempted to reconcile their differences with appellant prior to seeking court-ordered visitation; and (3) in finding that there was clear and convincing evidence that there was a significant and beneficial relationship between appellees and the children, that it would be in the children's best interests for such a relationship to continue, and that the continuation of the relationship would not adversely impact appellant's relationship with the children, and in ordering grandparent visitation.
With respect to the second assignment of error regarding whether the parties attempted to reconcile their differences regarding visitation prior to appellees' seeking court-ordered visitation, we note that appellant's brief includes no argument regarding this assigned error. Errors that are assigned but not argued will not be addressed by an appellate court. Borley Storage & Transfer Co. v. Whitted, 271 Neb. 84, 710 N.W.2d 71 (2006). Accordingly, we do not consider this assignment of error.

IV. STANDARDS OF REVIEW
Whether a statute is constitutional is a question of law; accordingly, the Nebraska Supreme Court is obligated to reach a conclusion independent of the decision reached by the court below. In re Interest of Phoenix L., 270 Neb. 870, 708 N.W.2d 786 (2006).
Determinations concerning grandparent visitation are initially entrusted to the discretion of the trial judge, whose determinations, on appeal, will be reviewed de novo on the record and affirmed in the absence of abuse of the trial judge's discretion. Nelson v. Nelson, 267 Neb. 362, 674 N.W.2d 473 (2004). A judicial abuse of discretion exists when a *519 judge, within the effective limits of authorized judicial power, elects to act or refrain from action, but the selected option results in a decision which is untenable and unfairly deprives a litigant of a substantial right or a just result in matters submitted for disposition through the judicial system. Id.

V. ANALYSIS

1. COMPARISON OF NEBRASKA'S GRANDPARENT VISITATION STATUTES, §§ 43-1801 TO 43-1803, TO STANDARDS UNDER TROXEL

Appellant asserts that Nebraska's grandparent visitation statutes, §§ 43-1801 to 43-1803, are unconstitutional on their face and as applied, because, given her parental rights, they violate her substantive due process rights under both the U.S. and the Nebraska Constitutions. Relying upon the U.S. Supreme Court's decision in Troxel v. Granville, 530 U.S. 57, 120 S.Ct. 2054, 147 L.Ed.2d 49 (2000), appellant claims that the grandparent visitation statutes are unconstitutional in that they fail to give adequate deference to a fit parent's decisions regarding the care, custody, and control of the parent's minor children and permit a court to order grandparent visitation over the objection of such parent. As discussed in the final section of our analysis, we conclude that the Nebraska grandparent visitation statutes as applied to appellant did not violate her substantive due process rights. Further, since there exists a set of circumstances under which the statutes are valid, §§ 43-1801 to 43-1803 are not unconstitutional on their face. We therefore conclude that the district court did not err when it rejected appellant's constitutional challenge.

(a) The U.S. Supreme Court's Decision in Troxel

Appellant's argument challenging the constitutionality of the Nebraska grandparent visitation statutes is based primarily upon the U.S. Supreme Court's decision in Troxel, in which the Court reviewed the constitutionality of the State of Washington's nonparent visitation statute that permitted "`[a]ny person' to petition a superior court for visitation rights `at any time,' and authorize[d] that court to grant such visitation rights whenever `visitation may serve the best interest of the child.'" 530 U.S. at 60, 120 S.Ct. 2054 (quoting Wash. Rev.Code Ann. § 26.10.160(3) (West 1997)). The U.S. Supreme Court concluded that the Washington statute at issue was unconstitutional.
According to the Troxel opinion, the grandparents in Troxel, following the death of their son, had sought two weekends of overnight visitation per month, as well as 2 weeks of visitation each summer, with their two grandchildren with whom they had had a longstanding relationship. The children's mother did not oppose all visitation, but, rather, sought to limit visitation to 1 day per month. After a trial, the trial court ruled in favor of the grandparents, stating that "`it is normally in the best interest of the children to spend quality time with the grandparent.'" 530 U.S. at 69, 120 S.Ct. 2054. The mother appealed, and the Washington Court of Appeals reversed, concluding that the grandparents lacked standing to seek visitation under the Washington statute unless a custody action was pending.
The grandparents sought further review, which was granted by the Washington Supreme Court. The Washington Supreme Court affirmed for different reasons. According to the U.S. Supreme Court, the Washington Supreme Court concluded that the state's nonparent visitation statute unconstitutionally infringed on the fundamental rights of parents to rear their children and held that the statute *520 was unconstitutional on its face. 530 U.S. at 63, 120 S.Ct. 2054, 530 U.S. at 76, 120 S.Ct. 2054 (Souter, J., concurring).
The U.S. Supreme Court granted certiorari and, in a plurality opinion, concluded that the Washington nonparent visitation statute violated the mother's substantive due process rights and was unconstitutional as applied in that case. Justice O'Connor wrote the opinion for the Court in Troxel, in which Chief Justice Rehnquist and Justices Ginsburg and Breyer joined.
In its analysis, the plurality opinion noted that the Court had "long recognized that the [14th] Amendment's Due Process Clause . . . `guarantees more than fair process.' . . . The Clause also includes a substantive component that `provides heightened protection against government interference with certain fundamental rights and liberty interests.'" Troxel v. Granville, 530 U.S. 57, 65, 120 S.Ct. 2054, 147 L.Ed.2d 49 (2000) (quoting Washington v. Glucksberg, 521 U.S. 702, 117 S.Ct. 2258, 138 L.Ed.2d 772 (1997)). The Court identified the liberty interest at issue in Troxel as the interest of parents in the care, custody, and control of their children, and stated that this interest was "perhaps the oldest of the fundamental liberty interests recognized by this Court." Troxel v. Granville, 530 U.S. at 65, 120 S.Ct. 2054 (citing Meyer v. Nebraska, 262 U.S. 390, 43 S.Ct. 625, 67 L.Ed. 1042 (1923) (stating that liberty interest protected by Due Process Clause includes parents' rights to "establish a home and bring up children" and "to control the education of their own")). See, also, Washington v. Glucksberg, 521 U.S. at 720, 117 S.Ct. 2258 (citing Meyer v. Nebraska, supra, and Pierce v. Society of Sisters, 268 U.S. 510, 45 S.Ct. 571, 69 L.Ed. 1070 (1925), and stating that "[i]n a long line of cases, we have held that, in addition to the specific freedoms protected by the Bill of Rights, the `liberty' specially protected by the Due Process Clause includes the right . . . to direct the education and upbringing of one's children"); Santosky v. Kramer, 455 U.S. 745, 753, 102 S.Ct. 1388, 71 L.Ed.2d 599 (1982) (discussing "[t]he fundamental liberty interest of natural parents in the care, custody, and management of their child"); Parham v. J. R., 442 U.S. 584, 602, 99 S.Ct. 2493, 61 L.Ed.2d 101 (1979) (stating that "[o]ur jurisprudence historically has reflected Western civilization concepts of the family as a unit with broad parental authority over minor children. Our cases have consistently followed that course"); Quilloin v. Walcott, 434 U.S. 246, 255, 98 S.Ct. 549, 54 L.Ed.2d 511 (1978) (stating that "[w]e have recognized on numerous occasions that the relationship between parent and child is constitutionally protected"); Wisconsin v. Yoder, 406 U.S. 205, 232, 92 S.Ct. 1526, 32 L.Ed.2d 15 (1972) (stating that "[t]he history and culture of Western civilization reflect a strong tradition of parental concern for the nurture and upbringing of their children. This primary role of the parents in the upbringing of their children is now established beyond debate as an enduring American tradition"); Stanley v. Illinois, 405 U.S. 645, 651, 92 S.Ct. 1208, 31 L.Ed.2d 551 (1972) (stating that "[i]t is plain that the interest of a parent in the companionship, care, custody, and management of his or her children `come[s] to this Court with a momentum for respect lacking when appeal is made to liberties which derive merely from shifting economic arrangements'" (citation omitted)). The Court summarized these cases, stating: "In light of this extensive precedent, it cannot now be doubted that the Due Process Clause of the Fourteenth Amendment protects the fundamental right of parents to make decisions concerning the care, custody, and control of their children." Troxel v. *521 Granville, 530 U.S. 57, 66, 120 S.Ct. 2054, 147 L.Ed.2d 49 (2000). We have recognized the fundamental rights of parents in Nebraska cases. See, In re Guardianship of D.J., 268 Neb. 239, 682 N.W.2d 238 (2004); Uhing v. Uhing, 241 Neb. 368, 488 N.W.2d 366 (1992).
After reviewing its history of recognizing a parent's right to make decisions concerning the care, custody, and control of his or her children, the Court found the Washington statute, as applied, unconstitutionally infringed upon this right. Troxel v. Granville, supra. The plurality found it significant that the Washington statute, which the Court described as "breathtakingly broad," entirely excluded the parents from the visitation decisionmaking process, noting that
[o]nce the visitation petition has been filed in court and the matter placed before a judge, a parent's decision that visitation would not be in the child's best interest is accorded no deference. [The Washington visitation statute] contains no requirement that a court accord the parent's decision any presumption of validity or any weight whatsoever. Instead, the Washington statute places the best-interest determination solely in the hands of the judge.
530 U.S. at 67, 120 S.Ct. 2054.
After discussing the fact that the grandparents in Troxel had not alleged either that the mother was an unfit parent or that she had decided to cut off visitation entirely, the Court concluded that the "Due Process Clause does not permit a State to infringe on the fundamental right of parents to make child rearing decisions simply because a state judge believes a `better' decision could be made" and declared the Washington statute unconstitutional as applied. 530 U.S. at 73, 120 S.Ct. 2054. We observe that by virtue of the act of invalidating the Washington statute, the Court in Troxel exercised constitutional oversight in an area in which the state had intervened in the parent-child relationship, and we further observe that we have previously approved of the propriety of such oversight. See In re Adoption of Baby Girl H., 262 Neb. 775, 635 N.W.2d 256 (2001).
In its decision concluding that the Washington statute infringed on the "fundamental right of parents," the Court in Troxel did not articulate the level of scrutiny it applied. Moreover, the Court highlighted the circumspect nature of its opinion and noted that it was not defining a specific test by which to evaluate the constitutionality of nonparental visitation statutes. The Court stated:
Because we rest our decision on the sweeping breadth of [the Washington statute] and the application of that broad, unlimited power in this case, we do not consider the primary constitutional question passed on by the Washington Supreme Courtwhether the Due Process Clause requires all nonparental visitation statutes to include a showing of harm or potential harm to the child [if visitation is withheld]. We do not, and need not, define today the precise scope of the parental due process right in the visitation context. In this respect, we agree with [the dissenting opinion of] Justice Kennedy that the constitutionality of a standard for awarding visitation turns on the specific manner in which that standard is applied and that the constitutional protections in this area are best "elaborated with care." . . . Because much state-court adjudication in this context occurs on a case-by-case basis, we would be hesitant to hold that specific nonparental visitation statutes violate the Due Process Clause as a per se matter. *522 Troxel v. Granville, 530 U.S. 57, 73, 120 S.Ct. 2054, 147 L.Ed.2d 49 (2000).
Justice Souter concurred in the Court's judgment but would have affirmed on the basis that the visitation statute was facially invalid. Id. (Souter, J., concurring in the judgment). Justice Thomas also concurred in the judgment, noting that the Court had failed to identify the "appropriate standard of review." 530 U.S. at 80, 120 S.Ct. 2054 (Thomas, J., concurring in the judgment). Justice Thomas would have struck down the Washington statute under a strict scrutiny analysis. Id.
Justices Stevens, Scalia, and Kennedy each dissented on different grounds. Justice Stevens criticized the Washington Supreme Court's analysis relative to the "any person" provision and the statute's absence of a provision requiring a finding of harm to the child if visitation was withheld, preferring an as applied analysis rather than resolution of constitutionality based on a facial analysis. Id. (Stevens, J., dissenting). Justice Scalia would have reversed the Washington Supreme Court's decision. He described the "parental rights" at issue as unenumerated and stated that he would prefer that the area of family law implicated in Troxel be prescribed by state legislatures and not the federal judiciary. Id. (Scalia, J., dissenting). Justice Kennedy stated that the 14th Amendment included a substantive due process right to parent children without undue state interference, but he recognized the potential for tension between this right and the best interests of the child. Justice Kennedy would have remanded the cause to the state courts to engage in an "as applied" analysis. Troxel v. Granville, supra (Kennedy, J., dissenting).
The Troxel plurality decision for the most part was limited to the specific infirmities of the State of Washington visitation statute as applied to the facts in that case. It has been observed, and we agree, that the Troxel Court left to state courts the task of developing the law relative to the resolution of child visitation disputes arising between a parent and nonparent. See Denise v. Tencer, 46 Va.App. 372, 617 S.E.2d 413 (2005). We note that since the Troxel decision, the U.S. Supreme Court has declined additional opportunities to define the scope of a parent's due process right in the nonparent visitation context, which may mean that state courts are expected to adjudicate the matter on a case-by-case basis. See, Robinson v. Ford-Robinson, No. 04-1235, 362 Ark. 232, 2005 WL 1041158 (May 5, 2005), cert. denied ___ U.S. ___, 126 S.Ct. 424, ___ L.Ed.2d ___; Galjour v. Harris, 795 So.2d 350 (La.App.2001), cert. denied 534 U.S. 1020, 122 S.Ct. 545, 151 L.Ed.2d 422; Blixt v. Blixt, 437 Mass. 649, 774 N.E.2d 1052 (2002), cert. denied 537 U.S. 1189, 123 S.Ct. 1259, 154 L.Ed.2d 1022 (2003); Moriarty v. Bradt, 177 N.J. 84, 827 A.2d 203 (2003), cert. denied 540 U.S. 1177, 124 S.Ct. 1408, 158 L.Ed.2d 78 (2004); Harrold v. Collier, 107 Ohio St.3d 44, 836 N.E.2d 1165 (2005), cert. denied ___ U.S. ___, 126 S.Ct. 1474, 164 L.Ed.2d 248 (2006).
The lack of a precise standard in Troxel has been criticized by some authorities. See, e.g., Developments in the Law  The Law of Marriage and Family, IV. Changing Realities of Parenthood: The Law's Response to the Evolving American Family and Emerging Reproductive Technologies, 116 Harv. L.Rev. 2052, 2056 (2003) (stating that "[t]he plurality opinion in Troxel, one of six opinions issued in the case, failed to deliver a clear, unambiguous standard under which to assess nonparental visitation statutes and has been the source of much confusion and debate"); Paula A. Lorfeld, Comment, Have State Judiciaries Become Legislatures When *523 Grandma Comes to Court?: State Court Decisions in the Post-Troxel Era, 5 Marq. Elder's Advisor 241, 242 (2004) (referring to Troxel "opinion's vagueness"). Nonetheless, other authorities have identified certain guiding principles in Troxel. Chief among these principles is a recognition that inherent in the Court's refusal to globally hold that "nonparental visitation statutes violate [parental substantive due process rights] and the Due Process Clause as a per se matter," Troxel v. Granville, 530 U.S. 57, 73, 120 S.Ct. 2054, 147 L.Ed.2d 49 (2000), is a tacit approval of nonparental visitation statutes that meet substantive due process imperatives. See Developments in the Law  The Law of Marriage and Family, supra. See, also, Blixt v. Blixt, supra; Deem v. Lobato, 136 N.M. 266, 96 P.3d 1186 (Ct.App.2004).
Despite the absence from Troxel of precisely enunciated criteria for awarding nonparental visitation in the face of parental disapproval, the Court offered guidance on several points when considering the constitutionality of statutes governing nonparental visitation. First, in determining whether the nonparental visitation should occur, the plurality opinion declared that "there is a presumption that fit parents act in the best interests of their children." 530 U.S. at 68, 120 S.Ct. 2054.
Second, the plurality opinion stated that "if a fit parent's decision of the kind at issue here becomes subject to judicial review, the court must accord at least some special weight to the parent's own determination." 530 U.S. at 70, 120 S.Ct. 2054. The Troxel Court did not explain the nature of this "special weight." See, Robinson v. Ford-Robinson, No. 04-1235, 362 Ark. 232, 2005 WL 1041158 (May 5, 2005), cert. denied ___ U.S. ___, 126 S.Ct. 424, ___ L.Ed.2d ___; In re R.A., Jr., 121 P.3d 295 (Colo.App.2005). Nonetheless, several authorities have defined it as a degree of "deference" to the parents' decision. Developments in the Law  The Law of Marriage and Family, supra at 2057; Blixt v. Blixt, supra; Blakely v. Blakely, 83 S.W.3d 537 (Mo.2002).
Third, the Troxel Court noted the failure of the Washington trial court to base its order awarding grandparent visitation "on any special factors that might justify the State's interference with [the parent's] fundamental right to make decisions concerning the rearing of her [children.]" 530 U.S. at 68, 120 S.Ct. 2054. It has been observed that this comment indicates that there are factors that might override a parent's decision and, therefore, implicit in Troxel is the underlying recognition of the "rebuttable" nature of the presumption that fit parents act in their children's best interests. See Troxel v. Granville, supra (Stevens, J., dissenting). Although not expressly stated in the plurality opinion, the Troxel Court's acknowledgment that this presumption can be rebutted with the appropriate evidence has been noted by many authorities. See In re R.A., Jr., 121 P.3d at 298 (stating that "[c]ourts recognize that, in light of the rebuttable nature of the presumption [that fit parents act in their children's best interests], the `special weight' requirement does not insulate parental wishes from judicial review"). See, also, Deem v. Lobato, 136 N.M. 266, 270, 96 P.3d 1186, 1190 (N.M.App.2004) (stating that "[t]here is nothing in Troxel or the resulting case law to suggest that the Supreme Court considered the presumption that a fit parent acts in the best interests of his or her child to be other than a rebuttable presumption"); Harrold v. Collier, 107 Ohio St.3d 44, 51, 836 N.E.2d 1165, 1172 (2005), cert. denied ___ U.S. ___, 126 S.Ct. 1474, 164 L.Ed.2d 248 (2006) (stating that "while Troxel states that there is a presumption that fit parents act in the best interest of their children, nothing in Troxel indicates *524 that this presumption is irrefutable"). Accord Crafton v. Gibson, 752 N.E.2d 78, 96-97 (Ind.App.2001) (stating that under Troxel, "a grandparent seeking visitation has the burden of rebutting the presumption that a decision made by a fit parent to deny or limit visitation was made in the child's best interest").
In summary, certain principles emerge from the plurality opinion in Troxel v. Granville, 530 U.S. 57, 120 S.Ct. 2054, 147 L.Ed.2d 49 (2000), with respect to a parent's due process rights in the context of a nonparent visitation statute that are useful for our current analysis. Those principles are as follows:
(1) There is a presumption that fit parents act in the best interests of their children.
(2) In light of this presumption, a fit parent's decision concerning the denial of grandparent visitation must be accorded at least some special weight.
(3) Notwithstanding the special weight to be accorded a fit parent's decision, the presumption in favor of fit parents is rebuttable under the appropriate circumstances. With the guidance of these three principles, we examine Nebraska's grandparent visitation statutes.

(b) Consideration of Nebraska's Grandparent Visitation Statutes Under the Principles in Troxel and as Compared to the Washington Statute in Troxel

As noted above, appellant brings a substantive due process challenge to the Nebraska grandparent visitation statutes under both the U.S. and the Nebraska Constitutions. Substantive due process relates to the content of the statute specifying when a right can be lost or impaired. In re Adoption of Baby Girl H., 262 Neb. 775, 635 N.W.2d 256 (2001). Appellant argues in effect that when considered under the principles outlined in Troxel and when compared to the Washington statute in Troxel, the Nebraska grandparent visitation statutes show the same weaknesses as the Washington statute and that, therefore, the Nebraska statutes impermissibly impair her parental rights.
The federal and state Constitutions contain similar due process language, and both provide that no person shall be deprived of life, liberty, or property without due process of law. U.S. Const. amend. XIV; Neb. Const. art. I, § 3. In the context of a right to privacy, we have effectively stated that the due process provision of the Nebraska Constitution is congruent with the federal Constitution and that the Nebraska Constitution does not contain any rights broader than the federal Constitution. See State v. Senters, 270 Neb. 19, 699 N.W.2d 810 (2005) (stating that due process clause of Nebraska Constitution does not contain right of privacy broader than that recognized under federal Constitution). We extend the foregoing principle of congruence to the present context involving a parent's substantive due process rights, and accordingly, we do not distinguish between the two constitutions in our analysis.
Appellant raises both a facial and an "as applied" due process challenge, and as explained in the last section of our analysis, we conclude that the grandparent visitation statutes are constitutional as applied to appellant, and it therefore follows that the statutes at issue are not facially invalid. The U.S. Supreme Court has stated that "[a] facial challenge to a legislative Act is . . . the most difficult challenge to mount successfully, since the challenger must establish that no set of circumstances exists under which the Act would be valid." United States v. Salerno, 481 U.S. 739, 745, 107 S.Ct. 2095, 95 L.Ed.2d 697 (1987). See, also, State v. *525 Sanders, 269 Neb. 895, 697 N.W.2d 657 (2005) (describing facial challenge as asserting no valid application of statute exists because statute is unconstitutional on its face). A facial challenge is contrasted to a challenge to a statute "as applied" to the individual. See State v. Sanders, supra.
In considering the constitutionality of Nebraska's grandparent visitation statutes, we are guided by certain well-established principles and presumptions. The burden of establishing the unconstitutionality of a statute is on the one attacking its validity. Chase v. Neth, 269 Neb. 882, 697 N.W.2d 675 (2005); State ex rel. Stenberg v. Omaha Expo. & Racing, 263 Neb. 991, 644 N.W.2d 563 (2002). A statute is presumed to be constitutional, and all reasonable doubts will be resolved in favor of its constitutionality. Chase v. Neth, supra. See, also, Pony Lake Sch. Dist. v. State Committee for Reorg., 271 Neb. 173, 710 N.W.2d 609 (2006). It is the duty of a court to give a statute an interpretation that meets constitutional requirements if it can reasonably be done. State ex rel. Stenberg v. Moore, 258 Neb. 199, 602 N.W.2d 465 (1999). The unconstitutionality of a statute must be clearly demonstrated before a court can declare the statute unconstitutional. Chase v. Neth, supra; Ponderosa Ridge LLC v. Banner County, 250 Neb. 944, 554 N.W.2d 151 (1996).
At common law in Nebraska and elsewhere, "`grandparents lacked any legal right to visitation and communication with their grandchildren if such visitation was forbidden by the parents. . . . Indeed, the parents' obligation to allow such visitation was a moral, not a legal obligation.'" Pier v. Bolles, 257 Neb. 120, 124, 596 N.W.2d 1, 4 (1999) (quoting Ex Parte Bronstein, 434 So.2d 780 (Ala.1983)). In part due to changing demographics and the presence of single-parent households in which grandparents and other persons "outside the nuclear family are called upon with increasing frequency to assist in the everyday tasks of child rearing," Troxel v. Granville, 530 U.S. 57, 64, 120 S.Ct. 2054, 147 L.Ed.2d 49 (2000), and in part due to a recognition of "the importance of the grandparent-grandchild relationship in the lives of children," Moriarty v. Bradt, 177 N.J. 84, 97, 827 A.2d 203, 210 (2003), cert. denied 540 U.S. 1177, 124 S.Ct. 1408, 158 L.Ed.2d 78 (2004) (citing Chrystal C. Ramirez Barranti, The Grandparent/Grandchild Relationship: Family Resource in an Era of Voluntary Bonds, 34 Fam. Rel. 343 (1985)), every state has adopted a statutory scheme permitting grandparent visitation under varying circumstances. Pier v. Bolles, supra (citing 3 Family Law and Practice § 32.09[7][b][ii] (Arnold H. Rutkin ed., 1999)). The circumstances under which grandparents can seek and retain visitation differ widely from state to state. Id.
Nebraska was the last state in the nation to grant grandparent visitation. Judiciary Committee Hearing, L.B. 105, 89th Leg., 1st Sess. 91 (Mar. 25, 1985). In 1986, the grandparent visitation statutes, 1986 Neb. Laws, L.B. 105, were enacted by the Nebraska Legislature, setting forth the grandparents' statutory visitation scheme. See, §§ 43-1801 to 43-1803; Pier v. Bolles, supra. The circumstances in which a grandparent can seek visitation are covered by § 43-1802 of the grandparent visitation statutes, which provides in relevant part as follows:
(1) A grandparent may seek visitation with his or her minor grandchild if:
(a) The child's parent or parents are deceased;
(b) The marriage of the child's parents has been dissolved or petition for the dissolution of such marriage has *526 been filed, is still pending, but no decree has been entered; or
(c) The parents of the minor child have never been married but paternity has been legally established.
(2) In determining whether a grandparent shall be granted visitation, the court shall require evidence concerning the beneficial nature of the relationship of the grandparent to the child. The evidence may be presented by affidavit and shall demonstrate that a significant beneficial relationship exists, or has existed in the past, between the grandparent and the child and that it would be in the best interests of the child to allow such relationship to continue. Reasonable rights of visitation may be granted when the court determines by clear and convincing evidence that there is, or has been, a significant beneficial relationship between the grandparent and the child, that it is in the best interests of the child that such relationship continue, and that such visitation will not adversely interfere with the parent-child relationship.
Synthesizing the requirements of § 43-1802(2), we have stated that under the Nebraska grandparent visitation statutes, a court is without authority to order grandparent visitation unless a petitioning grandparent can prove by clear and convincing evidence that "`(1) [t]here is, or has been, a significant beneficial relationship between the grandparent and the child; (2) it is in the best interests of the child that such relationship continue; and (3) such visitation will not adversely interfere with the parent-child relationship.'" Nelson v. Nelson, 267 Neb. 362, 369, 674 N.W.2d 473, 479 (2004) (quoting Eberspacher v. Hulme, 248 Neb. 202, 533 N.W.2d 103 (1995)).
Although the Nebraska grandparent visitation statutes allow court intrusion upon the parent-child relationship, it is important to note that as part of its "legislative findings," the Nebraska Legislature recognized that "[t]he state presumes the critical importance of the parent-child relationship and the child-parent relationship in the welfare and development of the minor child . . . ." Neb.Rev.Stat. § 43-2902 (Reissue 2004). So, too, with regard to the importance of the parent-child relationship, this court has stated that
"parents and their children have a recognized unique and legal interest in, and a constitutionally protected right to, companionship and care as a consequence of the parent-child relationship, a relationship that, in the absence of parental unfitness or a compelling state interest, is entitled to protection from intrusion into that relationship."
In re Guardianship of D.J., 268 Neb. 239, 246, 682 N.W.2d 238, 244 (2004) (quoting Uhing v. Uhing, 241 Neb. 368, 488 N.W.2d 366 (1992)). The importance of the parent-child relationship is reflected in the language of § 43-1802(2), which requires that a grant of grandparent visitation "not adversely interfere with the parent-child relationship" and that any such grant be proved by clear and convincing evidence, which burden is higher than that in conventional civil cases. See, Schuelke v. Wilson, 255 Neb. 726, 587 N.W.2d 369 (1998); In re Kindra S., 14 Neb.App. 202, 705 N.W.2d 792 (2005). See, also, Beal v. Endsley, 3 Neb.App. 589, 529 N.W.2d 125 (1995).
In connection with appellant's challenge to the constitutionality of the Nebraska grandparent visitation statutes due to their purported intrusion into her parent-child relationship, she urges us to utilize a strict scrutiny review of the grandparent visitation statutes. "Under strict scrutiny review, the law must be justified by a compelling governmental interest and must be narrowly tailored to *527 advance that interest." Douglas Cty. v. Anaya, 269 Neb. 552, 556, 694 N.W.2d 601, 605 (2005). As noted above, in concluding that the Washington nonparent visitation statute was unconstitutional as applied, the plurality opinion in Troxel v. Granville, 530 U.S. 57, 120 S.Ct. 2054, 147 L.Ed.2d 49 (2000), refrained from announcing the level of scrutiny it was applying. Since Troxel, state courts have debated the level of scrutiny to apply to challenges to nonparent visitation statutes. Some states have elected to apply the heightened level of analysis of strict scrutiny. See, Roth v. Weston, 259 Conn. 202, 789 A.2d 431 (2002); Blixt v. Blixt, 437 Mass. 649, 774 N.E.2d 1052 (2002), cert. denied 537 U.S. 1189, 123 S.Ct. 1259, 154 L.Ed.2d 1022 (2003); Rideout v. Riendeau, 761 A.2d 291 (Me.2000); Moriarty v. Bradt, 177 N.J. 84, 827 A.2d 203 (2003), cert. denied 540 U.S. 1177, 124 S.Ct. 1408, 158 L.Ed.2d 78 (2004); Harrold v. Collier, 107 Ohio St.3d 44, 836 N.E.2d 1165 (2005), cert. denied ___ U.S. ___, 126 S.Ct. 1474, 164 L.Ed.2d 248 (2006). Other states have opted to apply a lower level of review such as a rational basis analysis. See, Crafton v. Gibson, 752 N.E.2d 78 (Ind.App.2001); Blakely v. Blakely, 83 S.W.3d 537 (Mo. 2002). We conclude that given the fundamental nature of the parental rights that are claimed to have been intruded upon by the grandparent visitation statutes, a strict scrutiny level of analysis is appropriate.
We read appellant's argument as claiming that the provisions of Nebraska's grandparent visitation statutes are sufficiently broad as to be comparable to the Washington statute that was disapproved in Troxel. Such an argument naturally invites a comparison of Nebraska's statutes to the provisions of the Washington statute, an approach we note that numerous other state courts have utilized when considering constitutional challenges to their respective grandparent visitation statutes. See, Rideout v. Riendeau, supra; Blakely v. Blakely, supra; Moriarty v. Bradt, supra; Harrold v. Collier, supra; Glidden v. Conley, 175 Vt. 111, 820 A.2d 197 (2003); State ex rel. Brandon L. v. Moats, 209 W.Va. 752, 551 S.E.2d 674 (2001).
Comparing Nebraska's statutes to the Washington statute in Troxel, we conclude that contrary to appellant's assertion, Nebraska's statutes are more narrowly drawn than the Washington statute and explicitly protect parental rights while taking the child's best interests into consideration. Unlike the Washington statute that allowed "[a]ny person" to petition the court for visitation rights "at any time," the Nebraska grandparent visitation statutes limit the parties who can petition the court for visitation. Section 43-1802 permits only grandparents to seek visitation, and a "grandparent" is defined under § 43-1801 to include only "the biological or adoptive parent of a minor child's biological or adoptive parent." Further, a Nebraska grandparent can seek visitation only under certain circumstances. Under § 43-1802(1), a grandparent may seek visitation if the grandchild's parent or parents are deceased, divorced or in the process of seeking a divorce, or have never been married but paternity has been legally established.
We further note that the Nebraska grandparent visitation statutes, unlike the Washington statute at issue in Troxel, provide that the grandparent seeking visitation must prove by clear and convincing evidence that "there is, or has been, a significant beneficial relationship between the grandparent and the child, that it is in the best interests of the child that such relationship continue, and that such visitation will not adversely interfere with the parent-child relationship." § 43-1802(2). We believe that unlike the Washington *528 statute, these provisions satisfy the Troxel principles that a fit parent is presumed to act in the best interests of his or her child, and although special weight is to be accorded a fit parent's decision regarding visitation, the presumption in favor of a parent's decision is rebuttable. Thus, although the Nebraska grandparent visitation statutes recognize the interests of the child in the continuation of the grandparent relationship, under Nebraska's grandparent visitation statutes as a whole, the best interests of the child consideration does not deprive the parent of sufficient protection, because visitation will not be awarded where such visitation would adversely interfere with the parent-child relationship. See Troxel v. Granville, 530 U.S. 57, 70, 120 S.Ct. 2054, 147 L.Ed.2d 49 (2000) (citing with approval § 43-1802(2) as providing "protection for [the parent's] fundamental constitutional right to make decisions concerning the rearing of [the parent's own children]"). In view of the foregoing comparison, we reject appellant's assertion that Nebraska's grandparent visitation statutes fail to meet the principles in Troxel and suffer from the weaknesses of the Washington statute, which weaknesses led the U.S. Supreme Court to disapprove of the Washington statute. We therefore proceed to an examination of the record in this case and an assessment of the grandparent visitation statutes as they were applied to appellant.

2. APPLICATION OF THE NEBRASKA GRANDPARENT VISITATION STATUTES: REVIEW OF THE DISTRICT COURT'S DECISION ORDERING GRANDPARENT VISITATION
Appellant claims that the district court erred in ordering grandparent visitation in this case. Specifically, appellant claims that appellees failed to produce clear and convincing evidence that grandparent visitation would be in the children's best interests and that such visitation would not adversely interfere with her parent-child relationship.
This court has previously recognized that "Nebraska's grandparent visitation statutes clearly and significantly place the burden of proof upon the grandparent seeking a visitation order." Nelson v. Nelson, 267 Neb. 362, 369, 674 N.W.2d 473, 479 (2004). Pursuant to the grandparent visitation statutes, a district court cannot order grandparent visitation unless
a petitioning grandparent proves by clear and convincing evidence that "(1) [t]here is, or has been, a significant beneficial relationship between the grandparent and the child; (2) it is in the best interests of the child that such relationship continue; and (3) such visitation will not adversely interfere with the parent-child relationship."
267 Neb. at 369, 674 N.W.2d at 479 (quoting Eberspacher v. Hulme, 248 Neb. 202, 533 N.W.2d 103 (1995)). Clear and convincing evidence is that amount of evidence which produces in the trier of fact a firm belief or conviction about the existence of a fact to be proved. In re Interest of Jagger L., 270 Neb. 828, 708 N.W.2d 802 (2006).
Turning to the first statutory requirement, we note that in appellant's brief, she does not argue that there has not been a significant beneficial relationship between appellees and the grandchildren. Moreover, the record contains ample evidence upon which to base a qualitative assessment of the personal relationship that existed between appellees and the grandchildren, both prior to the filing of the grandparent visitation petition and thereafter. As noted by the district court:
A plethora of individuals . . . testified as to the close relationship which they had observed between [appellees] and the minor children . . . . [Appellees] were *529 the owners of the Wallace Flying Service where Jeremy . . . worked and [appellant] worked. The office of the airport was frequently used, especially during the summer months when Jeremy. . . was flying from daylight to sundown, to care for the minor children. [Appellee] Linda Hamit would take care of the boys, feed them and play with them when Jeremy was flying. The children had bicycles and toys, as well as a sand-pile outside the office. Between the months of April and August, the children would be at the airport until dark. The boys would eat with [appellees] and the other pilots.
After the separation . . . Jeremy . . . had the boys every other week, [and] the boys would be at the residence of [appellees] two or three times per week. There were a lot of toys, and the boys would frequently eat at the residence of [appellees]. [Appellees] also own a horse which the boys would ride. The oldest child, Wyatt, would frequently go to the post office with his grandfather. [Appellees] also own a dog which Wyatt considered to be his.
A number of individuals testified at trial that there was a close, affectionate, and loving relationship between both boys and [appellees].
The record also contains the testimony of Dr. Lisa Jones, a licensed clinical psychologist, who testified as to her observations of appellees and their grandchildren during several visitations in the fall of 2004. She testified that "[t]here was a lot of physical contact, either in terms of being held in and snuggled in arms or, again, being held and helped in [activities], just lots of very physical affectionate contact between the boys and the grandparents." She described appellees' home as "very cognizant of the children's needs. For example, they have a room that is set up with toys and two beds and a crib where, obviously, that's the children's room, where they can nap, if they need to, or they can play or they can enjoy themselves. . . ." She testified that at one of her later observations, when the children were more comfortable with her presence, she asked Wyatt whether he "like[d] visiting [appellees.] And he stated, Yes. I then asked him if he was scared to go visit with them, and he gave me a very strange look and he said no. And that was significant to me because, again, he looked at me like, that's a silly question."
In summary, appellees presented ample evidence of the nature of their relationship with Wyatt and Garrett, and that such relationship was beneficial to the children. Given this record, there is clear and convincing evidence to support the trial court's finding that appellees have a significant beneficial relationship with Wyatt and Garrett. Further, in view of the record, it cannot be said that the district court abused its discretion in finding by clear and convincing evidence that it is in the best interests of Wyatt and Garrett for their relationship with appellees to continue.
We next review the evidence relative to the requirement that grandparent visitation not adversely interfere with the parent-child relationship. In this regard, Jones testified to the effect that she had not "notice[d] anything from [appellees] that would indicate that [they are] harboring resentment that is carrying over into [the grandchildren's] visitation." Numerous witnesses testified that they had never heard appellees speak negatively regarding appellant in the presence of Wyatt and Garrett. Appellee Carl Hamit testified to the effect that during visitation with his grandchildren, he had not discussed appellant or the litigation and that his focus was on the grandchildren and spending time *530 with them. Both appellees testified to the effect that they had no animosity toward appellant. Moreover, the record contains evidence that appellees have attempted to comply with appellant's directions concerning the care of Wyatt and Garrett. Both appellees testified that at times, appellant would request that the children be returned early from their court-ordered visits with appellees, and appellees would accommodate her requests. Jones testified that during one of her observations, Wyatt had asked his grandfather, appellee Carl Hamit, to take the plane to go look at deer, and appellee had told Wyatt that they were going to take the truck. Jones noted that this was in accordance with appellant's expressed desire not to have the children on a plane and stated that "that was significant in terms of respecting that [request]."
There is clear and convincing evidence that visitation by appellees would not adversely interfere with the parent-child relationship between appellant and her children. Referring to the record, it is clear that the relationship between appellant and appellees is strained and that appellant does not encourage a relationship between appellees and the grandchildren. Nevertheless it cannot be said that the record shows that the visitation adversely interferes in the relationship that exists between appellant and her children.
In support of her argument that the district court abused its discretion in ordering grandparent visitation in this case, appellant relies in part upon the testimony of Jane Canell, a mental health therapist, who was called as an expert witness by appellant. In summary, Canell testified that Wyatt was afraid of appellees, that he felt appellees were trying to take him away from appellant, and that he did not want to visit them. The district court stated that "[b]ased upon [its] observation of the demeanor of the witnesses while testifying, [the court] reject[ed] virtually all of the negative testimony by Jane Canell," as "not believable." In this regard, the district court noted certain discrepancies in Canell's office notes, and further noted that Canell had never observed the grandchildren with appellees or talked to appellees. We have frequently recognized that "this court will consider the fact that the trial court saw and heard the witnesses and observed their demeanor while testifying, and will give great weight to the trial court's judgment as to credibility." General Fiberglass Supply v. Roemer, 256 Neb. 810, 815, 594 N.W.2d 283, 287 (1999). See, In re Guardianship of Robert D., 269 Neb. 820, 696 N.W.2d 461 (2005); In re Estate of Craven, 265 Neb. 41, 654 N.W.2d 196 (2002). In view of the district court's judgment regarding credibility, we reject appellant's invitation to consider Canell's testimony as outweighing other witnesses in the case.
The district court awarded visitation consisting of one 10-hour visitation every month and 7 consecutive days in the summer. In view of the record and the ages of the children, we do not find this ruling to be an abuse of discretion.

3. RESOLUTION
We have reviewed the record in this case, and we note that there is no allegation that appellant was an unfit parent. The district court honored the presumption in Troxel v. Granville, 530 U.S. 57, 120 S.Ct. 2054, 147 L.Ed.2d 49 (2000), that a fit parent acts in the best interests of his or her child, and appropriately placed on appellees the burden of proving by clear and convincing evidence the requirements of § 43-1802(2). In addition, the record reflects that although it did not use the Troxel words, "special weight," the district court gave special weight to *531 appellant's decision concerning visitation. The district court treated appellant's decision as a rebuttable presumption of best interests, thereby protecting appellant's fundamental rights before ultimately determining that it was in the children's best interests to grant visitation to appellees. The district court's decision is consistent with Troxel, is narrowly tailored to meet the state's compelling interest in protecting the well-being of its children, see Shoecraft v. Catholic Social Servs. Bureau, 222 Neb. 574, 385 N.W.2d 448 (1986), and is constitutional under a strict scrutiny analysis. Furthermore, the specific visitation awarded was appropriate.
Given the record in this case, we conclude that Nebraska's grandparent visitation statutes, §§ 43-1801 to 43-1803, are constitutional as applied to appellant in this case. Further, since there exists a set of circumstances under which the statutes are valid, §§ 43-1801 to 43-1803 are not unconstitutional on their face. See United States v. Salerno, 481 U.S. 739, 107 S.Ct. 2095, 95 L.Ed.2d 697 (1987). Additionally, the specific visitation awarded to appellees was not an abuse of discretion. We find no merit to appellant's assignments of error, and we affirm the decision of the district court concluding that the provisions of §§ 43-1801 to 43-1803 are constitutional and awarding specified visitation to appellees.

VI. CONCLUSION
For the reasons stated above, we affirm the district court's order concluding that Nebraska's grandparent visitation statutes are not violative of appellant's substantive due process rights and are constitutional. Given the record in this case, we conclude the district court did not abuse its discretion, and we affirm the district court's order awarding grandparent visitation in favor of appellees.
AFFIRMED.
WRIGHT, J., not participating.
