AN EXTRAGRADIENT TYPE METHOD FOR A SYSTEM OF EQUILIBRIUM PROBLEMS, VARIATIONAL INEQUALITY PROBLEMS AND FIXED POINTS OF FINITELY MANY NONEXPANSIVE MAPPINGS

Thanyarat Jitpeera; Poom Kumam

AN EXTRAGRADIENT TYPE METHOD FOR A SYSTEM OF EQUILIBRIUM PROBLEMS, VARIATIONAL INEQUALITY PROBLEMS AND FIXED POINTS OF FINITELY MANY NONEXPANSIVE MAPPINGS

Authors

Thanyarat Jitpeera DEPARTMENT OF MATHEMATICS, FACULTY OF SCIENCE, KING MONGKUT'S UNIVERSITY OF TECHNOLOGYTHONBURI (KMUTT), BANGKOK 10140
Poom Kumam DEPARTMENT OF MATHEMATICS, FACULTY OF SCIENCE, KING MONGKUT'S UNIVERSITY OF TECHNOLOGYTHONBURI (KMUTT), BANGKOK 10140

Keywords:

Nonexpansive mapping, Monotone mapping, Variational inequality, Fixed points, System of equilibrium problems, Extragradient approximation method

Abstract

The purpose of this paper is to investigate the problem of finding the common element of the set of common fixed points of a finite family of nonexpansive mappings, the set of solutions of a system of equilibrium problems and the set of solutions of the variational inequality problem for a monotone and k-Lipschitz continuous mapping in Hilbert spaces. Consequently, we obtain the strong convergence theorem of the proposed iterative algorithm to the unique solutions of variational inequality, which is the optimality condition for a minimization problem. The results presented in this paper generalize, improve and extend some well-known results in the literature.