SOLVING SYSTEM OF SPLIT COMMON FIXED POINT AND MONOTONE VARIATIONAL INCLUSION PROBLEMS VIA DYNAMICAL STEP-SIZE IN BANACH SPACES

Abstract

In this paper, we investigate a self adaptive accelerated method for solving splitcommon fixed point problem for a nite family of firmly-nonexpansive type mappings (Type P) and monotone variational inclusion problem in p-uniformly convex and uniformly smooth Banach spaces. Using a modified Halpern method together with an inertial extrapolation method, we prove a strong convergence theorem for solving the aforementioned problems.The implementation of our iterative method does not require prior knowledge of the operator norm. We also provide some numerical examples to show better performance of our method.Our results extend and complement many related results existing in the literature.