Convexity in G-metric spaces and approximation of fixed points by Mann iterative proces

TL;DR

This paper introduces convexity in G-metric spaces and employs Mann iterative processes to establish convergence results for fixed point approximation, extending existing theorems to this new setting.

Contribution

It defines convexity in G-metric spaces and applies Mann iterative processes to prove convergence, extending fixed point results to this novel context.

Findings

Established convexity in G-metric spaces.

Proved convergence of Mann iterative process in convex G-metric spaces.

Extended fixed point existence results to this new setting.

Abstract

In this paper, we first define the concept of convexity in G-metric spaces. We then use Mann iterative process in this newly defined convex G-metric space to prove some convergence results for some classes of mappings. In this way, we can extend several existence results to those approximating fixed points. Our results are just new in the setting.