Open Access Research

Strong convergence theorems by hybrid projection methods for equilibrium problems and fixed point problems of the asymptotically quasi-ϕ-nonexpansive mappings

Jong Kyu Kim

Author Affiliations

Department of Mathematics, Kyungnam University, Masan, Kyungnam 631-701, Korea

Fixed Point Theory and Applications 2011, 2011:10  doi:10.1186/1687-1812-2011-10

Published: 24 June 2011

Abstract

We consider a hybrid projection method for finding a common element in the fixed point set of an asymptotically quasi-ϕ-nonexpansive mapping and in the solution set of an equilibrium problem. Strong convergence theorems of common elements are established in a uniformly smooth and strictly convex Banach space which has the Kadec-Klee property.

2000 Mathematics subject classification: 47H05, 47H09, 47H10, 47J25

Keywords:
Asymptotically quasi-ϕ-nonexpansive mapping; Relatively non-expansive mapping; Generalized projection; Equilibrium problem; Lower semi-continuous