A Unified Iterative Algorithm for Variational-like Inequalities and Fixed Point Problems in Banach Space with Applications to Image Denoising

Abstract

This paper introduces and analyzes an inertial projection iterative scheme for solving combined generalized general variational-like inequality problem (CGGVLIP), the zero problem associated with a γ-inverse strongly monotone mapping, and the common fixed-point problem of a finite family of relatively nonexpansive mappings in two-uniformly convex and uniformly smooth Banach spaces. Strong convergence of the proposed algorithm to a common solution is established. The efficiency of the method is illustrated through numerical examples and validated via detailed figures. An application to image denoising is also presented to demonstrate its practical utility.