New Fixed Point Results over Orthogonal $\mathcal{F}$-Metric Spaces and Application in Second-Order Differential Equations

Abstract

In this article, we introduce the notion of cyclic $α$-admissible mapping with respect to $θ$ with its special cases, which are cyclic $α$-admissible mapping with respect to $θ^∗$ and cyclic $α^∗$-admissible mapping with respect to $θ.$ We present the notion of orthogonal $(αθ−βF)$-rational contraction and establish new fixed point results over orthogonal $\mathcal{F}$-metric space. The study includes illustrative examples to support our results. We apply our results to prove the existence and uniqueness of solutions for second-order differential equations.