Approximation of fixed points for a representation of nonexpansive mappings in Banach spaces

TL;DR

This paper introduces an implicit iterative scheme to approximate fixed points of nonexpansive mappings in smooth, uniformly convex Banach spaces, extending previous algorithms to broader settings.

Contribution

It develops a new implicit algorithm for fixed point approximation that generalizes earlier methods to more complex Banach space representations.

Findings

The scheme converges under specified conditions.

It extends previous algorithms to broader Banach space classes.

Provides theoretical convergence proofs.

Abstract

The purpose of this paper is to study an implicit scheme for a representation of nonexpansive mappings on a closed convex subset of a smooth and uniformly convex Banach space with respect to a left regular sequence of means defined on an appropriate space of bounded real valued functions of the semigroup. This algorithm extends the algorithm that introduced in [N. Hussain, M. L. Bami and E. Soori, An implicit method for finding a common fixed point of a representation of nonexpansive mappings in Banach spaces, Fixed Point Theory and Applications 2014, 2014:238].