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Viscosity extragradient method with Armijo linesearch rule for pseudomonotone equilibrium problem and fixed point problem in Hilbert spaces

Author

Listed:
  • Gaobo Li

    (Shan Dong Women’s University)

  • Yanxia Lu

    (North China Electric Power University)

  • Yeol Je Cho

    (Gyeongsang National University
    University of Electronic Science and Technology of China)

Abstract

In this paper, we introduce a viscosity extragradient method with Armijo linesearch rule to find a common element of solution set of a pseudomonotone equilibrium problem and fixed point set of a nonexpansive nonself-mapping in Hilbert space. The strong convergence of the algorithm is proved. As the application, a common fixed point theorem for two nonexpansive nonself-mappings is proved. Finally, some numerical examples are given to illustrate the effectiveness of the algorithm. Our result improves the ones of others in the literature.

Suggested Citation

  • Gaobo Li & Yanxia Lu & Yeol Je Cho, 2019. "Viscosity extragradient method with Armijo linesearch rule for pseudomonotone equilibrium problem and fixed point problem in Hilbert spaces," Indian Journal of Pure and Applied Mathematics, Springer, vol. 50(4), pages 903-921, December.
    • Handle: RePEc:spr:indpam:v:50:y:2019:i:4:d:10.1007_s13226-019-0363-2
    DOI: 10.1007/s13226-019-0363-2
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    References listed on IDEAS

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    1. P. Anh & H. Le Thi, 2013. "An Armijo-type method for pseudomonotone equilibrium problems and its applications," Journal of Global Optimization, Springer, vol. 57(3), pages 803-820, November.
    2. Miller, Naomi & Ruszczynski, Andrzej, 2008. "Risk-adjusted probability measures in portfolio optimization with coherent measures of risk," European Journal of Operational Research, Elsevier, vol. 191(1), pages 193-206, November.
    3. Dong, June & Zhang, Ding & Nagurney, Anna, 2004. "A supply chain network equilibrium model with random demands," European Journal of Operational Research, Elsevier, vol. 156(1), pages 194-212, July.
    4. Francisco Facchinei & Christian Kanzow, 2010. "Generalized Nash Equilibrium Problems," Annals of Operations Research, Springer, vol. 175(1), pages 177-211, March.
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    Cited by:

    1. Thidaporn Seangwattana & Somyot Plubtieng & Kanokwan Sitthithakerngkiet, 2021. "A new linesearch iterative scheme for finding a common solution of split equilibrium and fixed point problems," Indian Journal of Pure and Applied Mathematics, Springer, vol. 52(2), pages 614-628, June.

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