Inertial Halpern-type method for solving monotone variational inequality and fixed point problems in Banach spaces

Abstract

In this paper, we introduce inertial Tseng’s method and Halperntype algorithm for solving monotone variational inequality and fixed point problems in 2-uniformly convex and 2-uniformly smooth real Banach spaces. We establish strong convergence of our proposed method under some assumptions on parameters without knowledge of the operator norm. Finally, we give numerical experiments to illustrate the efficiency of our main result.