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System of Variational Inclusions and Fixed Points of Pseudocontractive Mappings in Banach Spaces

Author

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  • Lu-Chuan Ceng

    (Department of Mathematics, Shanghai Normal University, Shanghai 200234, China)

  • Mihai Postolache

    (Center for General Education, China Medical University, Taichung 40402, Taiwan
    Romanian Academy, Gh. Mihoc-C. Iacob Institute of Mathematical Statistics and Applied Mathematics, Bucharest 050711, Romania
    University “Politehnica” of Bucharest, Department of Mathematics and Informatics, Bucharest 060042, Romania)

  • Xiaolong Qin

    (Institute of Fundamental and Frontier Sciences, University of Electronic Science and Technology of China, Chengdu 611731, China)

  • Yonghong Yao

    (School of Mathematical Sciences, Tianjin Polytechnic University, Tianjin 300387, China)

Abstract

The purpose of this paper is to solve the general system of variational inclusions (GSVI) with hierarchical variational inequality (HVI) constraint, for an infinite family of continuous pseudocontractive mappings in Banach spaces. By utilizing the equivalence between the GSVI and the fixed point problem, we construct an implicit multiple-viscosity approximation method for solving the GSVI. Under very mild conditions, we prove the strong convergence of the proposed method to a solution of the GSVI with the HVI constraint, for infinitely many pseudocontractions.

Suggested Citation

  • Lu-Chuan Ceng & Mihai Postolache & Xiaolong Qin & Yonghong Yao, 2018. "System of Variational Inclusions and Fixed Points of Pseudocontractive Mappings in Banach Spaces," Mathematics, MDPI, vol. 7(1), pages 1-14, December.
    • Handle: RePEc:gam:jmathe:v:7:y:2018:i:1:p:5-:d:192132
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    References listed on IDEAS

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    1. Lu-Chuan Ceng & Abdul Latif & Abdullah E. Al-Mazrooei, 2014. "Iterative Algorithms for Systems of Generalized Equilibrium Problems with the Constraints of Variational Inclusion and Fixed Point Problems," Abstract and Applied Analysis, Hindawi, vol. 2014, pages 1-24, March.
    2. Lu-Chuan Ceng & Chang-yu Wang & Jen-Chih Yao, 2008. "Strong convergence theorems by a relaxed extragradient method for a general system of variational inequalities," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 67(3), pages 375-390, June.
    3. Lu-Chuan Ceng & Qamrul Ansari & Siegfried Schaible, 2012. "Hybrid extragradient-like methods for generalized mixed equilibrium problems, systems of generalized equilibrium problems and optimization problems," Journal of Global Optimization, Springer, vol. 53(1), pages 69-96, May.
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