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A New Hybrid Algorithm for a Pair of Quasi- 𠜙 -Asymptotically Nonexpansive Mappings and Generalized Mixed Equilibrium Problems in Banach Spaces

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  • Jinhua Zhu
  • Shih-Sen Chang

Abstract

The purpose of this paper is, by using a new hybrid method, to prove a strong convergence theorem for finding a common element of the set of solutions for a generalized mixed equilibrium problem, the set of solutions for a variational inequality problem, and the set of common fixed points for a pair of quasi- 𠜙 -asymptotically nonexpansive mappings. Under suitable conditions some strong convergence theorems are established in a 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, 2011. "A New Hybrid Algorithm for a Pair of Quasi- 𠜙 -Asymptotically Nonexpansive Mappings and Generalized Mixed Equilibrium Problems in Banach Spaces," International Journal of Mathematics and Mathematical Sciences, Hindawi, vol. 2011, pages 1-22, July.
    • Handle: RePEc:hin:jijmms:956852
    DOI: 10.1155/2011/956852
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