A self-adaptive iterative method for a split equality problem

Abstract

The purpose of this paper is to introduce an iterative algorithm for the split equality problem with an equilibrium problem, a variational inequality problem, and a fixed point problem of nonexpansive semigroups. We establish a strong convergence theorem of common solutions by the uniformly continuity rather than the Lipchitz continuity of the mappings in real Hilbert spaces. The proposed algorithm only requires one projection each per iteration onto the feasible sets. We also propose a self-adaptive technique that generates non-monotonic sequence of step sizes. Finally, we present a numerical example to illustrate the significance and efficient performance of our algorithm. Our results develop and unify several optimization results in the literature.