Strong Convergence Theorems for Countable Families of Uniformly Quasi‐ϕ‐Asymptotically Nonexpansive Mappings and a System of Generalized Mixed Equilibrium Problems

Siwaporn Saewan and Poom Kumam

Abstract and Applied Analysis, 2011, vol. 2011, issue 1

Abstract: 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 quasi‐ϕ‐asymptotically 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 iterative scheme converges strongly to a common element of the aforementioned sets. The results presented in this paper improve and extend important recent results in the literature.

Date: 2011
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https://doi.org/10.1155/2011/701675

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Persistent link: https://EconPapers.repec.org/RePEc:wly:jnlaaa:v:2011:y:2011:i:1:n:701675

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