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

Siwaporn Saewan and Poom Kumam

Abstract and Applied Analysis, 2011, vol. 2011, 1-27

Abstract:

The purpose of this paper is to present a new hybrid block iterative scheme by the generalized 𠑓 - projection method for finding a common element of the fixed point set for a countable family of uniformly quasi- 𠜙 -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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Persistent link: https://EconPapers.repec.org/RePEc:hin:jnlaaa:701675

DOI: 10.1155/2011/701675

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