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Common Solutions of Generalized Mixed Equilibrium Problems, Variational Inclusions, and Common Fixed Points for Nonexpansive Semigroups and Strictly Pseudocontractive Mappings

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  • Poom Kumam
  • Usa Hamphries
  • Phayap Katchang

Abstract

We introduce a new iterative scheme by shrinking projection method for finding a common element of the set of solutions of generalized mixed equilibrium problems, the set of common solutions of variational inclusion problems with set-valued maximal monotone mappings and inverse-strongly monotone mappings, the set of solutions of fixed points for nonexpansive semigroups, and the set of common fixed points for an infinite family of strictly pseudocontractive mappings in a real Hilbert space. We prove that the sequence converges strongly to a common element of the above four sets under some mind conditions. Furthermore, by using the above result, an iterative algorithm for solution of an optimization problem was obtained. Our results improve and extend the corresponding results of Martinez-Yanes and Xu (2006), Shehu (2011), Zhang et al. (2008), and many authors.

Suggested Citation

  • Poom Kumam & Usa Hamphries & Phayap Katchang, 2011. "Common Solutions of Generalized Mixed Equilibrium Problems, Variational Inclusions, and Common Fixed Points for Nonexpansive Semigroups and Strictly Pseudocontractive Mappings," Journal of Applied Mathematics, Hindawi, vol. 2011, pages 1-28, September.
    • Handle: RePEc:hin:jnljam:953903
    DOI: 10.1155/2011/953903
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    Cited by:

    1. Bashir Ali & G. C. Ugwunnadi, 2012. "Convergence Theorem for a Family of Generalized Asymptotically Nonexpansive Semigroup in Banach Spaces," International Journal of Mathematics and Mathematical Sciences, Hindawi, vol. 2012, pages 1-16, July.

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