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

Abstract

The purpose of this paper is to present a new hybrid block iterativescheme by the generalized $f$-projection method for finding a commonelement of the fixed point set for a countable family of uniformlyasymptotically quasi-$\phi$-nonexpansive mappings and the set ofsolutions of the system of generalized mixed equilibrium problems ina strictly convex and uniformly smooth Banach space with theKadec-Klee property. Furthermore, we prove that our new  hybridblock iterative scheme converges strongly to a common element of theafore mentioned sets. The results presented in this paper improveand extend important recent results in the literature.