Iterative Method for a Generalized Equilibrium Problem and Fixed Point Problem of Nonexpansive Mappings
Jitsupa Deepho, Issara Inchan, Suttirat Inma · 2010
In this paper, we introduce an iterative method for finding a common element of the set of solutions of a generalized equilibrium problem and the set of fixed points of a nonexpansive mapping in a Hilbert space. Then, we prove strong convergence theorems for nonexpansive mapping to solve a unique solution of the variational inequality. The results extended and improved the corresponding results of Y. Shehu [ Fixed point solutions of generalized equilibrium problems for nonexpansive mappings, J. Com. Appl. Math. doi:10.1016/j.cam.2010.01.055], and many others. Mathematics Subject Classification: 47H10, 47H09, 46B20