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A new linesearch iterative scheme for finding a common solution of split equilibrium and fixed point problems

Author

Listed:
  • Thidaporn Seangwattana

    (King Mongkut’s University of Technology North Bangkok)

  • Somyot Plubtieng

    (Naresuan University)

  • Kanokwan Sitthithakerngkiet

    (King Mongkut’s University of Technology North Bangkok (KMUTNB))

Abstract

In this paper, we propose a new linesearch iterative scheme for finding a common solution of split equilibrium and fixed point problems without pseudomonotonicity of the bifunction f in a real Hilbert space. When setting the solution of dual equilibrium problem is nonempty, we obtain a strong convergence theorem which is generated by the iterative scheme. Moreover, we also receive a new linesearch iterative scheme for finding a solution of the split equilibrium problem in suitable assumptions, and report some numerical results to illustrate the convergence of the proposed scheme.

Suggested Citation

  • 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.
    • Handle: RePEc:spr:indpam:v:52:y:2021:i:2:d:10.1007_s13226-021-00040-9
    DOI: 10.1007/s13226-021-00040-9
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    References listed on IDEAS

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    1. Prasit Cholamjiak & Suthep Suantai, 2013. "Iterative methods for solving equilibrium problems, variational inequalities and fixed points of nonexpansive semigroups," Journal of Global Optimization, Springer, vol. 57(4), pages 1277-1297, December.
    2. Jinzuo Chen & Mihai Postolache & Li-Jun Zhu, 2019. "Iterative Algorithms for Split Common Fixed Point Problem Involved in Pseudo-Contractive Operators without Lipschitz Assumption," Mathematics, MDPI, vol. 7(9), pages 1-13, August.
    3. A. Moudafi, 2011. "Split Monotone Variational Inclusions," Journal of Optimization Theory and Applications, Springer, vol. 150(2), pages 275-283, August.
    4. Bigi, Giancarlo & Castellani, Marco & Pappalardo, Massimo & Passacantando, Mauro, 2013. "Existence and solution methods for equilibria," European Journal of Operational Research, Elsevier, vol. 227(1), pages 1-11.
    5. 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.
    6. Sitthithakerngkiet, Kanokwan & Deepho, Jitsupa & Kumam, Poom, 2015. "A hybrid viscosity algorithm via modify the hybrid steepest descent method for solving the split variational inclusion in image reconstruction and fixed point problems," Applied Mathematics and Computation, Elsevier, vol. 250(C), pages 986-1001.
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