A hybrid iterative algorithm for a split mixed equilibrium problem and a hierarchical fixed point problem

Abstract

In this paper, we suggest and analyze a hybrid algorithm for finding a common solution of a split mixed equilibrium problem and a hierarcchical fixed point problem for a finite family of nonexpansive mappings. We prove the strong convergence of the iterative method under some mild conditions and derive some applications. Finally, we give a numerical example to justify the main results.