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Convergence analysis of a general iterative algorithm for finding a common solution of split variational inclusion and optimization problems

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Abstract

The purpose of this paper is to introduce a general iterative method for finding a common element of the set of common fixed points of an infinite family of nonexpansive mappings and the set of split variational inclusion problem in the framework Hilbert spaces. Strong convergence theorem of the sequences generated by the purpose iterative scheme is obtained. In the last section, we present some computational examples to illustrate the assumptions of the proposed algorithms.

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Acknowledgments

The authors are very thankful to the anonymous reviewers and editors for their careful reading of the manuscript and for their constructive reports, which have been very useful to improve the paper.

Funding

The authors acknowledge the financial support provided by King Mongkut’s University of Technology Thonburi through the “KMUTT 55th Anniversary Commemorative Fund”; also, this project was supported by the Theoretical and Computational Science (TaCS) Center under Computational and Applied Science for Smart Innovation Cluster (CLASSIC), Faculty of Science, KMUTT. Furthermore, the first author was supported by the Office of the Higher Education Commission (OHEC) and Thailand Research Fund (TRF) (Grant No.MRG6080123). Finally, Dr. Poom Kumam was supported by the Thailand Research Fund and the King Mongkut’s University of Technology Thonburi under the TRF Research Scholar Grant No.RSA6080047.

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Authors and Affiliations

  1. Nonlinear Dynamic Analysis Research Center, Faculty of Applied Science, Department of Mathematics, King Mongkut’s University of Technology North Bangkok (KMUTNB), Wongsawang, Bangsue, Bangkok, 10800, Thailand

    Kanokwan Sitthithakerngkiet

  2. Faculty of Science, Energy and Environment, King Mongkut’s University of Technology North Bangkok, Rayong Campus, 19 Moo 11, Tambon Nonglalok, Amphur Bankhai, Rayong, 21120, Thailand

    Jitsupa Deepho

  3. Faculty of Science, Department of Mathematics, University of Jaén, Campus Las Lagunillas, s/n, 23071, Jaén, Spain

    Juan Martínez-Moreno

  4. KMUTTFixed Point Research Laboratory, Faculty of Science, Department of Mathematics, King Mongkut’s University of Technology Thonburi (KMUTT), Room SCL 802 Fixed Point Laboratory, Science Laboratory Building, 126 Pracha Uthit Rd., Bang Mod, Thrung Khru, Bangkok, 10140, Thailand

    Poom Kumam

  5. KMUTT-Fixed Point Theory and Applications Research Group (KMUTT-FPTA), Theoretical and Computational Science Center (TaCS), Faculty of Science, King Mongkut’s University of Technology Thonburi (KMUTT), Science Laboratory Building, 126 Pracha Uthit Road, Bang Mod, Thung Khru, Bangkok, 10140, Thailand

    Poom Kumam

Authors
  1. Kanokwan Sitthithakerngkiet
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  2. Jitsupa Deepho
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  3. Juan Martínez-Moreno
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  4. Poom Kumam
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Correspondence to Poom Kumam.

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Sitthithakerngkiet, K., Deepho, J., Martínez-Moreno, J. et al. Convergence analysis of a general iterative algorithm for finding a common solution of split variational inclusion and optimization problems. Numer Algor 79, 801–824 (2018). https://doi.org/10.1007/s11075-017-0462-2

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  • DOI: https://doi.org/10.1007/s11075-017-0462-2

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