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

Author

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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, John Wiley & Sons, vol. 2013(1).
    • Handle: RePEc:wly:jnlaaa:v:2013:y:2013:i:1:n:430409
    DOI: 10.1155/2013/430409
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    References listed on IDEAS

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    1. Yonghong Yao & Rudong Chen & Giuseppe Marino & Yeong Cheng Liou, 2012. "Applications of Fixed-Point and Optimization Methods to the Multiple-Set Split Feasibility Problem," Journal of Applied Mathematics, Hindawi, vol. 2012, pages 1-21, April.
    2. Yonghong Yao & Rudong Chen & Giuseppe Marino & Yeong Cheng Liou, 2012. "Applications of Fixed‐Point and Optimization Methods to the Multiple‐Set Split Feasibility Problem," Journal of Applied Mathematics, John Wiley & Sons, vol. 2012(1).
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