Weak convergence theorems for symmetric generalized hybrid mappings in uniformly convex Banach spaces

TL;DR

This paper establishes weak convergence theorems for symmetric generalized hybrid mappings in uniformly convex Banach spaces, expanding fixed point theory using Banach limits and iterative methods.

Contribution

It introduces new weak convergence results for symmetric generalized hybrid mappings in Banach spaces, utilizing Banach limits and Ishikawa iteration.

Findings

Fixed point theorem for symmetric generalized hybrid mappings

Weak convergence theorems using Ishikawa iteration

Application of Banach limits in convergence proofs

Abstract

In this paper, we prove some theorems related to properties of generalized symmetric hybrid mappings in Banach spaces. Using Banach limits, we prove a fixed point theorem for symmetric generalized hybrid mappings in Banach spaces. Moreover, we prove some weak convergence theorems for such mappings by using Ishikawa iteration method in a uniformly convex Banach space.