Weak and Strong Convergence of Hybrid Subgradient Method for Pseudomonotone Equilibrium Problem and Two Finite Families of Multivalued Nonexpansive Mappings in Hilbert Spaces

Kiattisak Rattanaseeha

Abstract

In this paper,  we first introduce an iterative algorithm for finding  a common element of the set of solutions of a class of pseudomonotone equilibrium problems and the set of fixed points of two finite families of multivalued nonexpansive mappings in Hilbert space. Moreover, we prove that the proposed iterative algorithm converges weakly and strongly to a common element of the set of solutions of a class of pseudomonotone equilibrium problems and the set of fixed points of two finite families of multivalued nonexpansive mappings under some suitable conditions.