Existence and convergence of commutative mappings on some results of fixed point theory in a class of generalized non-expansive mappings

TL;DR

This paper introduces a broader class of commutative mappings satisfying generalized non-expansive conditions, extending existing fixed point results and exploring their properties in fixed point theory.

Contribution

It defines a new class of commutative mappings satisfying Condition B gamma mu, extending the scope of non-expansive mappings and their fixed point properties.

Findings

Extended fixed point results for generalized non-expansive mappings

Established properties of the new class of mappings

Broadened the applicability of fixed point theorems

Abstract

In this paper, we introduce a commutative mappings satisfying the class of generalized non-expansive mappings which is wider than the class of mappings satisfying the condition (C), so called Condition B gamma, mu. The results obtained in this paper extend and generalized non-expansive mappings and other results in this direction. Different properties and some fixed point results for the mappings are obtained here. Keywords: Non expansive mappings, Condition (C), Condition B gamma mu, Commuting mappings, Fixed point.