Best Proximity Point Results for Cyclic Orbital Contraction Mappings in $CAT_p(0)$ Metric Spaces

TL;DR

This paper introduces cyclic orbital contraction mappings in $CAT_p(0)$ spaces, establishing the existence of best proximity points and extending results to uniformly convex Banach spaces, advancing fixed point theory.

Contribution

It generalizes cyclic contraction mappings to cyclic orbital contraction mappings and proves their best proximity point existence in $CAT_p(0)$ and Banach spaces.

Findings

Existence of best proximity points in $CAT_p(0)$ spaces.

Extension of results to uniformly convex Banach spaces.

Generalization of cyclic contraction mappings.

Abstract

In this paper, we introduce the concept of cyclic orbital contraction mappings which generalizes the concept of cyclic contraction mappings. We establish the existence of best proximity point of these mappings in the framework of $CAT_p(0)$ metric spaces. Also, we study the existence of best proximity point theorems for cyclic orbital contraction mappings in uniformly convex Banach spaces.