Modified Inertial Forward–Backward Algorithm in Banach Spaces and Its Application

Abstract

In this paper, we present a new modified inertial forward–backward algorithm for finding a common solution of the quasi-variational inclusion problem and the variational inequality problem in a q-uniformly smooth Banach space. The proposed algorithm is based on descent, splitting and inertial ideas. Under suitable assumptions, we prove that the sequence generated by the iterative algorithm converges strongly to the unique solution of the abovementioned problems. Numerical examples are also given to demonstrate our results.