Accelerated Bregman projection rules for pseudomonotone variational inequalities and common fixed point problems

Let E be a p-uniformly convex and uniformly smooth Banach space, which is more general than Hilbert space. Let VIP and CFPP represent a variational inequality problem and the common fixed point problem of a Bregman relatively asymptotically nonexpansive mapping and a finite family of Bregman relatively nonexpansive mappings in E, respectively. In this paper, we put forward two accelerated Bregman projection algorithms with linesearch process for solving the two pseudomonotone VIPs and the CFPP. With the help of suitable assumptions, we prove weak and strong convergence of the suggested algorithms to a common solution of the two pseudomonotone VIPs and the CFPP, respectively. In the end, an illustrated instance is provided to back up the viability and performability of our proposed rules.