New Fixed Point Results over Orthogonal $\mathcal{F}$-Metric Spaces and Application in Second-Order Differential Equations
Year: 2024
Author: Mohammed M.A. Taleb, Saeed A.A. Al-Salehi, V.C. Borkar
Journal of Nonlinear Modeling and Analysis, Vol. 6 (2024), Iss. 3 : pp. 825–840
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.
Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.12150/jnma.2024.825
Journal of Nonlinear Modeling and Analysis, Vol. 6 (2024), Iss. 3 : pp. 825–840
Published online: 2024-01
AMS Subject Headings:
Copyright: COPYRIGHT: © Global Science Press
Pages: 16
Keywords: Fixed point orthogonal $(αθ −βF)$-rational contraction cyclic αadmissible mapping with respect to $θ $ orthogonal $\mathcal{F}$-metric space second-order differential equation.