A new algorithm for split variational inclusion and fixed point problems in Banach spaces

Abstract

In this article, we introduce a new algorithm for finding a solution element of the split variational inclusion problem which is also a fixed point of a nonexpansive mapping in a uniformly convex and smooth Banach space. A strong convergence theorem of the proposed algorithm is established under some suitable control conditions. Our main result can reduce to study several variational inclusion problems, null point problems, and fixed point problems in both Hilbert and Banach spaces. Numerical experiments to illustrate the convergence behavior of our proposed algorithm are given. Moreover, we also apply our results to solve the image restoration problems.