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Existence theorems and iterative approximation methods for generalized mixed equilibrium problems for a countable family of nonexpansive mappings

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  • Uthai Kamraksa
  • Rabian Wangkeeree

Abstract

In this paper, we introduce the new generalized mixed equilibrium problem basing on hemicontinuous and relaxed monotonic mapping. Using the KKM technique, we obtain the existence of solutions for the generalized mixed equilibrium problem in a Banach space. Furthermore, we also introduce a hybrid projection algorithm for finding a common element in the solution set of a generalized mixed equilibrium problem and the common fixed point set of a countable family of nonexpansive mappings. The strong convergence theorem of the proposed sequence is obtained in a Banach space setting. The main results extend various results existing in the current literature. Copyright Springer Science+Business Media, LLC. 2012

Suggested Citation

  • Uthai Kamraksa & Rabian Wangkeeree, 2012. "Existence theorems and iterative approximation methods for generalized mixed equilibrium problems for a countable family of nonexpansive mappings," Journal of Global Optimization, Springer, vol. 54(1), pages 27-46, September.
    • Handle: RePEc:spr:jglopt:v:54:y:2012:i:1:p:27-46
    DOI: 10.1007/s10898-011-9739-5
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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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