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An iterative algorithm for common fixed points for nonexpansive semigroups and strictly pseudo-contractive mappings with optimization problems

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Abstract

In this paper, we introduce an iterative algorithm for finding a common element of the set of solutions of a system of mixed equilibrium problems, the set of solutions of a variational inclusion problems for inverse strongly monotone mappings, the set of common fixed points for nonexpansive semigroups and the set of common fixed points for an infinite family of strictly pseudo-contractive mappings in Hilbert spaces. Furthermore, we prove a strong convergence theorem of the iterative sequence generated by the proposed iterative algorithm under some suitable conditions which solves some optimization problems. Our results extend and improve the recent results of Chang et al. (Appl Math Comput 216:51–60, 2010), Hao (Appl Math Comput 217(7):3000–3010, 2010), Jaiboon and Kumam (Nonlinear Anal 73:1180–1202, 2010) and many others.

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Authors and Affiliations

  1. Department of Mathematics and Statistics, Faculty of Science and Agricultural Technology, Rajamangala University of Technology Lanna Tak, Tak, 63000, Thailand

    Phayap Katchang

  2. Department of Mathematics, Faculty of Science, King Mongkut’s University of Technology Thonburi (KMUTT) Bangmod, Bangkok, 10140, Thailand

    Phayap Katchang & Poom Kumam

Authors
  1. Phayap Katchang
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  2. Poom Kumam
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Correspondence to Poom Kumam.

Additional information

The first author was supported by The KMUTT Post-doctoral scholarship at King Mongkut’s University of Technology Thonburi (KMUTT). Furthermore, The second author was supported by the Higher Education Research Promotion and National Research University Project of Thailand, Office of the Higher Education Commission (NRU-CSEC No. 55000613).

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Katchang, P., Kumam, P. An iterative algorithm for common fixed points for nonexpansive semigroups and strictly pseudo-contractive mappings with optimization problems. J Glob Optim 56, 1563–1589 (2013). https://doi.org/10.1007/s10898-012-9927-y

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  • DOI: https://doi.org/10.1007/s10898-012-9927-y

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