Generalization of The Results on Fixed Point For Coupling on Metric Spaces

TL;DR

This paper generalizes fixed point results for couplings in metric spaces by introducing new concepts like self-cyclic maps and Banach type g-couplings, extending prior work and proving existence theorems.

Contribution

It introduces self-cyclic maps, g-coupling, and Banach type g-coupling, extending fixed point theorems for coupled coincidence points in metric spaces.

Findings

Proves existence of coupled coincidence points for Banach type g-couplings.

Extends previous fixed point results by Choudhury et al.

Provides an example supporting the theoretical results.

Abstract

The purpose of this paper is to introduce the concept of self-cyclic maps, g-coupling and Banach type g-coupling which is the generalization of couplings introduced by Choudhury et al. In our main result we prove the existence theorem of coupled coincidence point for Banach type g-couplings which extends the results by Choudhury et al. We give an example in support of our result.