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Convergence Theorems for Common Solutions of Split Variational Inclusion and Systems of Equilibrium Problems

Author

Listed:
  • Yan Tang

    (College of Mathematics and Statistics, Chongqing Technology and Business University, Chongqing 400067, China)

  • Yeol Je Cho

    (Department of Mathematics Education, Gyeongsang National University, Jinju 52828, Korea
    School of Mathematical Sciences, University of Electronic Science and Technology of China, Chengdu 611731, China)

Abstract

In this paper, the split variational inclusion problem (SVIP) and the system of equilibrium problems (EP) are considered in Hilbert spaces. Inspired by the works of Byrne et al., López et al., Moudafi and Thukur, Sobumt and Plubtieng, Sitthithakerngkiet et al. and Eslamian and Fakhri, a new self-adaptive step size algorithm is proposed to find a common element of the solution set of the problems SVIP and EP. Convergence theorems are established under suitable conditions for the algorithm and application to the common solution of the fixed point problem, and the split convex optimization problem is considered. Finally, the performances and computational experiments are presented and a comparison with the related algorithms is provided to illustrate the efficiency and applicability of our new algorithms.

Suggested Citation

  • Yan Tang & Yeol Je Cho, 2019. "Convergence Theorems for Common Solutions of Split Variational Inclusion and Systems of Equilibrium Problems," Mathematics, MDPI, vol. 7(3), pages 1-25, March.
    • Handle: RePEc:gam:jmathe:v:7:y:2019:i:3:p:255-:d:213206
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    References listed on IDEAS

    as
    1. Yao, Yonghong & Cho, Yeol Je & Liou, Yeong-Cheng, 2011. "Algorithms of common solutions for variational inclusions, mixed equilibrium problems and fixed point problems," European Journal of Operational Research, Elsevier, vol. 212(2), pages 242-250, July.
    2. A. Moudafi, 2011. "Split Monotone Variational Inclusions," Journal of Optimization Theory and Applications, Springer, vol. 150(2), pages 275-283, August.
    3. 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, Hindawi, vol. 2013, pages 1-8, February.
    4. Zhao-Rong Kong & Lu-Chuan Ceng & Ching-Feng Wen, 2012. "Some Modified Extragradient Methods for Solving Split Feasibility and Fixed Point Problems," Abstract and Applied Analysis, Hindawi, vol. 2012, pages 1-32, December.
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