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Weak Convergence Theorem for Finding Fixed Points and Solution of Split Feasibility and Systems of Equilibrium Problems

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  • Kamonrat Sombut
  • Somyot Plubtieng

Abstract

The purpose of this paper is to introduce an iterative algorithm for finding a common element of the set of fixed points of quasi-nonexpansive mappings and the solution of split feasibility problems (SFP) and systems of equilibrium problems (SEP) in Hilbert spaces. We prove that the sequences generated by the proposed algorithm converge weakly to a common element of the fixed points set of quasi-nonexpansive mappings and the solution of split feasibility problems and systems of equilibrium problems under mild conditions. Our main result improves and extends the recent ones announced by Ceng et al. (2012) and many others.

Suggested Citation

  • Kamonrat Sombut & Somyot Plubtieng, 2013. "Weak Convergence Theorem for Finding Fixed Points and Solution of Split Feasibility and Systems of Equilibrium Problems," Abstract and Applied Analysis, Hindawi, vol. 2013, pages 1-8, February.
    • Handle: RePEc:hin:jnlaaa:430409
    DOI: 10.1155/2013/430409
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    Cited by:

    1. Yan Tang & Yeol Je Cho, 2019. "Convergence Theorems for Common Solutions of Split Variational Inclusion and Systems of Equilibrium Problems," Mathematics, MDPI, vol. 7(3), pages 1-25, March.

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