Accelerated Tseng’s Method for Finding Common Solution of Fixed Point, Variational Inequality and Zeros Problems in Reflexive Banach Spaces

Abstract

In this paper, we propose a novel accelerated extrapolation version of Tseng's algorithm with a self-adaptive step size for approximating a common solution to pseudomonotone variational inequality problems, zeros of maximal and Bregman inverse strongly monotone operators, and common fixed points of a finite family of Bregman demigeneralized mappings in a real reflexive Banach spaces. Using the Bregman distance technique, we establish a strong convergence result under mild assumptions, without requiring prior knowledge of the Lipschitz constant of the operator with application to a convex minimization problem (CMP). Our findings generalize and improve several results in the existing literature.