On the stability and convergence of Mann iteration process in convex A- metric spaces

TL;DR

This paper extends the analysis of Mann iteration convergence and stability to convex A-metric spaces, demonstrating convergence to fixed points of Zamfirescu type contractions and establishing stability results.

Contribution

It introduces convexity in A-metric spaces and proves convergence and stability of Mann iteration within this new framework, generalizing existing results.

Findings

Mann iteration converges to unique fixed points in convex A-metric spaces.

Stability of Mann iteration is established in convex A-metric spaces.

Results generalize known fixed point theorems to a new class of spaces.

Abstract

In this paper, firstly, we introduce the concept of convexity in A-metric spaces and show that Mann iteration process converges to the unique fixed point of Zamfirescu type contractions in this newly defined convex A-metric space. Secondly, we define the concept of stability in convex A-metric spaces and establish stability result for the Mann iteration process considered in such spaces. Our results carry some well-known results from the literature to convex A-metric spaces.