Strong convergence theorems by hybrid projection methods for equilibrium problems and fixed point problems of the asymptotically quasi-<it>&#981;</it>-nonexpansive mappings

Abstract

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-<it>&#981;</it>-nonexpansive mapping
• Relatively non-expansive mapping
• Generalized projection
• Equilibrium problem
• Lower semi-continuous