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.

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The Thai Journal of Mathematics organized and supported by The Mathematical Association of Thailand and Thailand Research Council and the Center for Promotion of Mathematical Research of Thailand (CEPMART).

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|ISSN 1686-0209|