TY - JOUR
T1 - New Fixed Point Results over Orthogonal $\mathcal{F}$-Metric Spaces and Application in Second-Order Differential Equations
AU - Taleb , Mohammed M.A.
AU - Al-Salehi , Saeed A.A.
AU - Borkar , V.C.
JO - Journal of Nonlinear Modeling and Analysis
VL - 3
SP - 825
EP - 840
PY - 2024
DA - 2024/08
SN - 6
DO - http://doi.org/10.12150/jnma.2024.825
UR - https://global-sci.org/intro/article_detail/jnma/23365.html
KW - Fixed point, orthogonal $(αθ −βF)$-rational contraction, cyclic αadmissible mapping with respect to $θ,$ orthogonal $\mathcal{F}$-metric space, second-order differential equation.
AB - <p style="text-align: justify;">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.</p>