Iterative Methods for Generalized Equilibrium Problems, Systems of General Generalized Equilibrium Problems and Fixed Point Problems for Nonexpansive Mappings in Hilbert Spaces

摘要

In this paper, we introduce a system of general generalized equilibrium problems and pro-pose an iterative scheme for finding the approximate solutions of a generalized equilibrium problem,a system of general generalized equilibrium problems and a fixed point problem of a nonexpansivemapping in a Hilbert space. We establish a strong convergence theorem for a sequence generated byour proposed iterative scheme to a common solution of these three problems. Utilizing this result, weprove three new strong convergence theorems for sequences generated by iterative schemes for fixedpoint problems, variational inequalities, equilibrium problems and systems of general generalizedequilibrium problems.