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A generalized forward–backward splitting method for solving a system of quasi variational inclusions in Banach spaces

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Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A. Matemáticas Aims and scope Submit manuscript

Abstract

The purpose of this paper is by using the generalized forward–backward splitting method and implicit midpoint rule to propose an iterative algorithm for finding a common element of the set of solutions to a system of quasi variational inclusions with accretive mappings and the set of fixed points for a \(\lambda \)-strict pseudo-contractive mapping in Banach spaces. Some strong convergence theorems of the sequence generated by the algorithm are proved. The results presented in the paper extend and improve some recent results. At the end of the paper, some applications to a system of variational inequalities problem, monotone variational inequalities, convex minimization problem and convexly constrained linear inverse problem are presented.

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Acknowledgements

The authors would like to express their thanks to the Editor and the Reviewers for their helpful comments and advices. This work was supported by the Natural Science Foundation of Center for General Education, China Medical University, Taichung, Taiwan and The Natural Science Foundation Research Center for Nonlinear Analysis and Optimization, Kaohsiung Medical University, Kaohsiung, 807, Taiwan.

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Authors and Affiliations

  1. Center for General Education, China Medical University, Taichung, 40402, Taiwan

    Shih-sen Chang & Jen-Chih Yao

  2. Center for Fundamental Science, and Research Center for Nonlinear Analysis and Optimization, Kaohsiung Medical University, Kaohsiung, 807, Taiwan

    Ching-Feng Wen

  3. Research Center for Nonlinear Analysis and Optimization, Kaohsiung Medical University, Kaohsiung, 807, Taiwan

    Jen-Chih Yao

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  1. Shih-sen Chang
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  2. Ching-Feng Wen
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  3. Jen-Chih Yao
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Correspondence to Shih-sen Chang.

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Chang, Ss., Wen, CF. & Yao, JC. A generalized forward–backward splitting method for solving a system of quasi variational inclusions in Banach spaces. RACSAM 113, 729–747 (2019). https://doi.org/10.1007/s13398-018-0511-2

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  • DOI: https://doi.org/10.1007/s13398-018-0511-2

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