Self-adaptive method for solving multiple set split equality variational inequality and fixed point problems in real Hilbert spaces

Abstract

In this article, we introduce the multiple-sets split equality variational inequality problem which includes the split feasibility problem, split variational inequality problem, split equality problem and multiple-sets split variational inequality problem to mention a few. Also, we prove a strong convergence theorem for approximation the solution of multiple-sets split equality variational inequality problem and fixed point problem of multi-valued quasi-nonepansive mappings in real Hilbert spaces using a modified Halpern iterative algorithm. The iterative algorithm employed in this paper is designed in such a way that its implementation does not require the estimation of the operator norms. Lastly, we present some consequences and a numerical example to illustrate the performance of our main result. Our result extends and complements many related results in the literature.