Convergence Theorem for Solving the Common Solution of System of
Generalized Equilibrium and Variational Inequality and Fixed Point
Problems with Application to Complementarity Problem
Assistant Professor Dr. Pongrus Phuangphoo, Ph.D.(Applied Mathematics)
Department of Mathematics, Faculty of Education, Bansomdejchaopraya Rajabhat University (BSRU)
Hiranruchi, Thonburi, Bangkok, Thailand, 10600.
([email protected] and [email protected])
Abstract
In this paper, we introduce an iterative procedure which is constructed by using the new hybrid projection method for solving the common solution for a variational inequality problem, a system of generalized equilibrium problems of inverse strongly monotone mappings and a system of bifunctions satisfying certain the conditions, and a fixed point problem for two countable families of weak relatively nonexpansive mapping. The strong convergence theorems are established on approximating a common solution of those problems in Banach space. Finally, we apply our the main results to complementarity problems and apply to a Hilbert space.
Keyword: convergence theorem, system of generalized equilibrium problem, fixed point problems, variational inequality problem, complementarity problems.
