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Strong Convergence Theorem for Solving Generalized Mixed Equilibrium Problems and Fixed Point Problems for Total Quasi- 𠜙 -Asymptotically Nonexpansive Mappings in Banach Spaces

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  • Zhaoli Ma
  • Lin Wang
  • Yunhe Zhao

Abstract

We introduce an iterative scheme for finding a common element of the set of solutions of generalized mixed equilibrium problems and the set of fixed points for countable families of total quasi- 𠜙 -asymptotically nonexpansive mappings in Banach spaces. We prove a strong convergence theorem of the iterative sequence generated by the proposed iterative algorithm in an uniformly smooth and strictly convex Banach space which also enjoys the Kadec-Klee property. The results presented in this paper improve and extend some recent corresponding results.

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  • Zhaoli Ma & Lin Wang & Yunhe Zhao, 2012. "Strong Convergence Theorem for Solving Generalized Mixed Equilibrium Problems and Fixed Point Problems for Total Quasi- 𠜙 -Asymptotically Nonexpansive Mappings in Banach Spaces," Journal of Applied Mathematics, Hindawi, vol. 2012, pages 1-21, June.
    • Handle: RePEc:hin:jnljam:506210
    DOI: 10.1155/2012/506210
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