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A New Construction and Convergence Analysis of Non-Monotonic Iterative Methods for Solving ρ -Demicontractive Fixed Point Problems and Variational Inequalities Involving Pseudomonotone Mapping

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  • Chainarong Khunpanuk

    (Mathematics and Computing Science Program, Faculty of Science and Technology, Phetchabun Rajabhat University, Phetchabun 67000, Thailand)

  • Bancha Panyanak

    (Research Group in Mathematics and Applied Mathematics, Department of Mathematics, Faculty of Science, Chiang Mai University, Chiang Mai 50200, Thailand
    Data Science Research Center, Department of Mathematics, Faculty of Science, Chiang Mai University, Chiang Mai 50200, Thailand)

  • Nuttapol Pakkaranang

    (Mathematics and Computing Science Program, Faculty of Science and Technology, Phetchabun Rajabhat University, Phetchabun 67000, Thailand)

Abstract

Two new inertial-type extragradient methods are proposed to find a numerical common solution to the variational inequality problem involving a pseudomonotone and Lipschitz continuous operator, as well as the fixed point problem in real Hilbert spaces with a ρ -demicontractive mapping. These inertial-type iterative methods use self-adaptive step size rules that do not require previous knowledge of the Lipschitz constant. We also show that the proposed methods strongly converge to a solution of the variational inequality and fixed point problems under appropriate standard test conditions. Finally, we present several numerical examples to show the effectiveness and validation of the proposed methods.

Suggested Citation

  • Chainarong Khunpanuk & Bancha Panyanak & Nuttapol Pakkaranang, 2022. "A New Construction and Convergence Analysis of Non-Monotonic Iterative Methods for Solving ρ -Demicontractive Fixed Point Problems and Variational Inequalities Involving Pseudomonotone Mapping," Mathematics, MDPI, vol. 10(4), pages 1-29, February.
    • Handle: RePEc:gam:jmathe:v:10:y:2022:i:4:p:623-:d:752017
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    References listed on IDEAS

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    1. Pasakorn Yordsorn & Poom Kumam & Habib ur Rehman & Abdulkarim Hassan Ibrahim, 2020. "A Weak Convergence Self-Adaptive Method for Solving Pseudomonotone Equilibrium Problems in a Real Hilbert Space," Mathematics, MDPI, vol. 8(7), pages 1-24, July.
    2. Xiaolong Qin & Nguyen Thai An, 2019. "Smoothing algorithms for computing the projection onto a Minkowski sum of convex sets," Computational Optimization and Applications, Springer, vol. 74(3), pages 821-850, December.
    3. Habib ur Rehman & Poom Kumam & Meshal Shutaywi & Nasser Aedh Alreshidi & Wiyada Kumam, 2020. "Inertial Optimization Based Two-Step Methods for Solving Equilibrium Problems with Applications in Variational Inequality Problems and Growth Control Equilibrium Models," Energies, MDPI, vol. 13(12), pages 1-28, June.
    4. Kassay, Gabor & Kolumban, Jozsef & Pales, Zsolt, 2002. "Factorization of Minty and Stampacchia variational inequality systems," European Journal of Operational Research, Elsevier, vol. 143(2), pages 377-389, December.
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