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Two new extragradient methods for solving equilibrium problems

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

Abstract

In this paper, we are concern with the classical equilibrium problem in real Hilbert spaces and introduce two new extragradient variants for it. By taking into account several fixed point theory techniques, we obtain simple structure methods that converge strongly and hence demonstrate the theoretical advantage of our methods. Moreover, our convergence assumptions are weaker than those assumed in related works in the literature. Primary numerical examples with comparisons illustrate the behaviour of our proposed scheme and show its advantages.

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Acknowledgements

The authors acknowledge the financial support provided by the Center of Excellence in Theoretical and Computational Science (TaCS-CoE), KMUTT. Moreover, this research project is supported by Thailand Science Research and Innovation (TSRI) Basic Research Fund: Fiscal year 2021 under project number 64A306000005. The authors acknowledge the financial support provided by the Center of Excellence in Theoretical and Computational Science (TaCS-CoE), KMUTT. The authors acknowledge the financial support provided by King Mongkut’s University of Technology North Bangkok, Contract no. KMUTNB-BasicR-64-22.

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Authors and Affiliations

  1. Fixed Point Research Laboratory, Fixed Point Theory and Applications Research Group, Center of Excellence in Theoretical and Computational Science (TaCS-CoE), Faculty of Science, King Mongkut’s University of Technology Thonburi (KMUTT), 126 Pracha Uthit Rd., Bang Mod, Thung Khru, Bangkok, 10140, Thailand

    Habib ur Rehman & Poom Kumam

  2. Department of Mathematics, ORT Braude College, 2161002, Karmiel, Israel

    Aviv Gibali

  3. The Center for Mathematics and Scientific Computation, U. Haifa, Mt. Carmel, Haifa, Israel

    Aviv Gibali

  4. Center of Excellence in Theoretical and Computational Science (TaCS-CoE), Faculty of Science, King Mongkut.s University of Technology Thonburi (KMUTT), 126 Pracha Uthit Rd., Bang Mod, Thung Khru, Bangkok, 10140, Thailand

    Poom Kumam

  5. Department of Medical Research, China Medical University Hospital, China Medical University, Taichung, 40402, Taiwan

    Poom Kumam

  6. Department of Mathematics, Faculty of Applied Science, Intelligent and Nonlinear Dynamic Innovations Research Center, King Mongkut’s University of Technology North Bangkok (KMUTNB), Bangkok, Thailand

    Kanokwan Sitthithakerngkiet

Authors
  1. Habib ur Rehman
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  2. Aviv Gibali
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  3. Poom Kumam
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  4. Kanokwan Sitthithakerngkiet
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Correspondence to Poom Kumam.

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Rehman, H.u., Gibali, A., Kumam, P. et al. Two new extragradient methods for solving equilibrium problems. RACSAM 115, 75 (2021). https://doi.org/10.1007/s13398-021-01017-3

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