New Fixed Point Results over Orthogonal $\mathcal{F}$-Metric Spaces and Application in Second-Order Differential Equations (Journal of Nonlinear Modeling and Analysis, 2024)
In this article, we introduce the notion of cyclic $α$-admissible mapping with respect to $θ$ with its special cases, which are cyclic $α$-admissiblemapping with respect to $θ^∗$ and cyclic $α^∗$-admissible mapping with respect to $θ.$ We present the notion of orthogonal $(αθ−βF)$-rational contraction andestablish new fixed point results over orthogonal $\mathcal{F}$-metric space. The studyincludes illustrative examples to support our results. We apply our results toprove the existence and uniqueness of solutions for second-order differentialequations.
Keywords: Fixed point; orthogonal $(αθ −βF)$-rational contraction; cyclic αadmissible mapping with respect to $θ; $ orthogonal $\mathcal{F}$-metric space; second-order differential equation.