Strong Convergence Theorems by Hybrid Block Generalized f-Projection Method for Fixed Point Problems of Asymptotically Quasi-ϕ-Nonexpansive Mappings and System of Generalized Mixed Equilibrium Problems
Siwaporn Saewan, Poom Kumam, Jong Kyu Kim · Thai Journal of Mathematics · 2013
The purpose of this paper is to present a new hybrid block iterative scheme by the generalized f-projection method for finding a common element of the fixed point set for a countable family of uniformly asymptotically quasi-φ- nonexpansive mappings and the set of solutions of the system of generalized mixed equilibrium problems in a strictly convex and uniformly smooth Banach space with the Kadec-Klee property. Furthermore, we prove that our new hybrid block iterative scheme converges strongly to a common element of the afore mentioned sets. The results presented in this paper improve and extend important recent results in the literature.