On Mann-type accelerated projection methods for pseudomonotone variational inequalities and common fixed points in Banach spaces

Abstract

In this paper, we investigate two Mann-type accelerated projection procedures with line search method for solving the pseudomonotone variational inequality (VIP) and the common fixed-point problem (CFPP) of finitely many Bregman relatively nonexpansive mappings and a Bregman relatively asymptotically nonexpansive mapping in $ p $-uniformly convex and uniformly smooth Banach spaces. Under mild conditions, we show weak and strong convergence of the proposed algorithms to a common solution of the VIP and CFPP, respectively.

Keywords

• pseudomonotone variational inequality
• mann-type accelerated projection method
• line-search method
• common fixed point
• bregman distance
• bregman projection