An iterative scheme for split equality equilibrium problems and split equality hierarchical fixed point problem

Abstract

Abstract This paper deals with a split equality equilibrium problem for pseudomonotone bifunctions and a split equality hierarchical fixed point problem for nonexpansive and quasinonexpansive mappings. We suggest and analyze an iterative scheme where the stepsizes do not depend on the operator norms, the so-called simultaneous projected subgradient-proximal iterative scheme for approximating a common solution of the split equality equilibrium problem and the split equality hierarchical fixed point problem. Further, we prove a weak convergence theorem for the sequences generated by this scheme. Furthermore, we discuss some consequences of the weak convergence theorem. We present a numerical example to justify the main result.

Keywords

• Split equality equilibrium problem
• Split equality hierarchical fixed point problem
• Simultaneous hybrid projected subgradient-proximal iterative scheme
• Quasinonexpansive mapping
• Pseudomonotone bifunction