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

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  • Siwaporn Saewan
  • Poom Kumam

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.

Suggested Citation

  • Siwaporn Saewan & Poom Kumam, 2011. "Strong Convergence Theorems for Countable Families of Uniformly Quasi- 𠜙 -Asymptotically Nonexpansive Mappings and a System of Generalized Mixed Equilibrium Problems," Abstract and Applied Analysis, Hindawi, vol. 2011, pages 1-27, August.
    • Handle: RePEc:hin:jnlaaa:701675
    DOI: 10.1155/2011/701675
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