Approximation of the Common Solution of Equilibrium Problems and Fixed Point Problems of Multi-valued Pseudocontractive-type Mappings in Hilbert Spaces

Abstract

A combined Ishikawa and Reich-Sabach iteration scheme is introduced in a real Hilbert spaceH for the approximation of the common solutions of equilibrium problems of bifunctions and fixed point problems of multi-valued pseudocontractivetype mappings. It is also proved that the iteration scheme converges strongly to a common element of the sets of fixed points of a finite family of multi-valued pseudocontractive-type mappings and the sets of solutions of a finite family of equilibrium problems. A numerical example for the computation of this algorithm is presented with concrete examples. The obtained results improve, complement and extend many results on equilibrium problems, multi-valued and single-valued mappings in the contemporary literature. AMS subject classification: 47H10, 54H25.