Extragradient Method for Generalized Mixed Equilibrium Problems and Fixed Point Problems of Finite Family of Nonexpansive Mapping
Issara Inchan · 2011
In this paper, we introduce the extragradient method for finding a common element of the set of solutions of generalized mixed equilibrium problem, the set of common fixed point of family of nonexpansive mappings the set of variational inequality for monotone, Lipschitz continuous mapping in a Hilbert space. Then we prove the strong convergence of iterative algorithm to a common element of this sets. The result extend and improve the result of Jian-Wen Peng and Jen-Chih Yao [Strong convergence theorems of iterative scheme based on the extragradient method for mixed equilibrium problems and fixed problems, Math. Comp. Modelling, 49(2009) 1816 - 1828.] Mathematics Subject Classification: 46C05, 47D03, 47H09, 47H10, 47H20