2010•Unpublished venueRequires access

Iterative Method for a Generalized Equilibrium Problem and Fixed Point Problem of Nonexpansive Mappings

Jitsupa Deepho, Issara Inchan, Suttirat Inma

Abstract

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

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Key concepts: Variational inequality, Fixed point, Hilbert space, Mathematics, Convergence (economics), Applied mathematics, Iterative method, Set (abstract data type)