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Applications to Solving Variational Inequality Problems via MR-Kannan Type Interpolative Contractions

Author

Listed:
  • Rizwan Anjum

    (Department of Mathematics, Division of Science and Technology, University of Education, Lahore 54770, Pakistan
    These authors contributed equally to this work.)

  • Andreea Fulga

    (Department of Mathematics and Computer Sciences, Transilvania University of Brasov, 500123 Brasov, Romania
    These authors contributed equally to this work.)

  • Muhammad Waqar Akram

    (Department of Mathematics, Division of Science and Technology, University of Education, Lahore 54770, Pakistan
    These authors contributed equally to this work.)

Abstract

The aim of this paper is manifold. We first define the new class of operators called MR-Kannan interpolative type contractions, which includes the Kannan, enriched Kannan, interpolative Kannan type, and enriched interpolative Kannan type operators. Secondly, we prove the existence of a unique fixed point for this class of operators. Thirdly, we study Ulam-Hyers stability, well-posedness, and periodic point properties. Finally, an application of the main results to the variational inequality problem is given.

Suggested Citation

  • Rizwan Anjum & Andreea Fulga & Muhammad Waqar Akram, 2023. "Applications to Solving Variational Inequality Problems via MR-Kannan Type Interpolative Contractions," Mathematics, MDPI, vol. 11(22), pages 1-11, November.
    • Handle: RePEc:gam:jmathe:v:11:y:2023:i:22:p:4694-:d:1283230
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    References listed on IDEAS

    as
    1. Erdal Karapınar & Andreea Fulga, 2019. "New Hybrid Contractions on b -Metric Spaces," Mathematics, MDPI, vol. 7(7), pages 1-15, June.
    2. Abbas, Mujahid & Anjum, Rizwan & Iqbal, Hira, 2022. "Generalized enriched cyclic contractions with application to generalized iterated function system," Chaos, Solitons & Fractals, Elsevier, vol. 154(C).
    3. Timilehin O. Alakoya & Oluwatosin T. Mewomo & Yekini Shehu, 2022. "Strong convergence results for quasimonotone variational inequalities," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 95(2), pages 249-279, April.
    Full references (including those not matched with items on IDEAS)

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