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A hybrid method for a family of relatively quasi-nonexpansive mappings and an equilibrium problem in Banach spaces

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  • Prasit Cholamjiak
  • Suthep Suantai

Abstract

We introduce a hybrid method for finding a common element in the solutions set of an equilibrium problem and the common fixed points set of a countable family of relatively quasi-nonexpansive mappings in a Banach space. A strong convergence theorem of the proposed method is established by using the concept of the Mosco convergence when the family {T n } satisfies the (*)-condition. The examples of three generated mappings which satisfy the (*)-condition are also given. Using the obtained result, we give some applications concerning the variational inequality problem and the convex minimization problem. Copyright Springer Science+Business Media, LLC. 2012

Suggested Citation

  • Prasit Cholamjiak & Suthep Suantai, 2012. "A hybrid method for a family of relatively quasi-nonexpansive mappings and an equilibrium problem in Banach spaces," Journal of Global Optimization, Springer, vol. 54(1), pages 83-100, September.
    • Handle: RePEc:spr:jglopt:v:54:y:2012:i:1:p:83-100
    DOI: 10.1007/s10898-011-9743-9
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    References listed on IDEAS

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    1. A. Tada & W. Takahashi, 2007. "Weak and Strong Convergence Theorems for a Nonexpansive Mapping and an Equilibrium Problem," Journal of Optimization Theory and Applications, Springer, vol. 133(3), pages 359-370, June.
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