New algorithms for solving pseudo-monotone variational inequalities in Banach spaces

Abstract

In this paper, we introduce new algorithms for finding a solution of a variational inequality problem involving pseudo-monotone operator which is also a fixed point of a Bregman relatively nonexpansive mapping in p-uniformly convex and uniformly smooth Banach spaces that are more general than Hilbert spaces. We prove weak and strong convergence theorems for proposed algorithms. Finally, we give some numerical experiments for supporting our main results.