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Generalized Mixed Equilibrium Problems and Fixed Point Problem for a Countable Family of Total Quasi- 𠜙 -Asymptotically Nonexpansive Mappings in Banach Spaces

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  • Jinhua Zhu
  • Shih-Sen Chang
  • Min Liu

Abstract

The purpose of this paper is first to introduce the concept of total quasi - 𠜙 - asymptotically nonexpansive mapping which contains many kinds of mappings as its special cases and then to use a hybrid algorithm to introduce a new iterative scheme for finding a common element of the set of solutions for a system of generalized mixed equilibrium problems and the set of common fixed points for a countable family of total quasi- 𠜙 -asymptotically nonexpansive mappings. Under suitable conditions some strong convergence theorems are established in an uniformly smooth and strictly convex Banach space with Kadec-Klee property. The results presented in the paper improve and extend some recent results.

Suggested Citation

  • Jinhua Zhu & Shih-Sen Chang & Min Liu, 2012. "Generalized Mixed Equilibrium Problems and Fixed Point Problem for a Countable Family of Total Quasi- 𠜙 -Asymptotically Nonexpansive Mappings in Banach Spaces," Journal of Applied Mathematics, Hindawi, vol. 2012, pages 1-22, December.
    • Handle: RePEc:hin:jnljam:961560
    DOI: 10.1155/2012/961560
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