Fixed Point Approximation for Enriched Suzuki Nonexpansive Mappings in Banach Spaces

Abstract

This paper investigates the approximation of fixed points for mappings that satisfy the enriched (C) condition using a modified iterative process in a Banach space framework. We first establish a weak convergence result and then derive strong convergence theorems under suitable assumptions. To illustrate the applicability of our findings, we present a numerical example involving mappings that satisfy the enriched (C) condition but not the standard (C) condition. Additionally, numerical computations and graphical representations demonstrate that the proposed iterative process achieves a faster convergence rate compared to several existing methods. As a practical application, we introduce a projection based an iterative process for solving split feasibility problems (SFPs) in a Hilbert space setting. Our findings contribute to the ongoing development of iterative processes for solving optimization and feasibility problems in mathematical and applied sciences.