Strong Convergence of an Iterative Method for Equilibrium Problems and Variational Inequality Problems
Hong Yu Li, Hong Zhi Li · Fixed Point Theory and Applications · 2009
Abstract We introduce an iterative method for finding a common element of the set of solutions of equilibrium problems, the set of solutions of variational inequality problems, and the set of fixed points of finite many nonexpansive mappings. We prove strong convergence of the iterative sequence generated by the proposed iterative algorithm to the unique solution of a variational inequality, which is the optimality condition for the minimization problem.