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Strong Convergence of a Hybrid Iteration Scheme for Equilibrium Problems, Variational Inequality Problems and Common Fixed Point Problems, of Quasi- ϕ -Asymptotically Nonexpansive Mappings in Banach Spaces

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  • Jing Zhao

Abstract

We introduce an iterative algorithm for finding a common element of the set of common fixed points of a finite family of closed quasi- ϕ -asymptotically nonexpansive mappings, the set of solutions of an equilibrium problem, and the set of solutions of the variational inequality problem for a γ -inverse strongly monotone mapping in Banach spaces. Then we study the strong convergence of the algorithm. Our results improve and extend the corresponding results announced by many others.

Suggested Citation

  • Jing Zhao, 2012. "Strong Convergence of a Hybrid Iteration Scheme for Equilibrium Problems, Variational Inequality Problems and Common Fixed Point Problems, of Quasi- ϕ -Asymptotically Nonexpansive Mappings in Banach S," Journal of Applied Mathematics, Hindawi, vol. 2012, pages 1-19, July.
    • Handle: RePEc:hin:jnljam:516897
    DOI: 10.1155/2012/516897
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