Accelerated Tseng’s Method for Finding Common Solution of Fixed Point, Variational Inequality and Zeros Problems in Reflexive Banach Spaces (European Journal of Pure and Applied Mathematics, 2026)
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.
Keywords: Variational Inequality Problem; Inertial term; Bregman Distance; Tseng's Method; Strong Convergence; Reflexive Banach Space; Common Fixed Point