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The Existence of Solutions to Nonlinear Matrix Equations via Fixed Points of Multivalued F -Contractions

Author

Listed:
  • Nawab Hussain

    (Department of Mathematics, King Abdulaziz University, P.O. Box 80203, Jeddah 21589, Saudi Arabia)

  • Ghada Ali

    (Department of Mathematics, King Abdulaziz University, P.O. Box 80203, Jeddah 21589, Saudi Arabia)

  • Iram Iqbal

    (Department of Mathematics, University of Sargodha, Sargodha 40100, Pakistan)

  • Bessem Samet

    (Department of Mathematics, College of Science, King Saud University, P.O. Box 2455, Riyadh 11451, Saudi Arabia)

Abstract

In this paper, we set up an adequate condition for the presence of a solution of the nonlinear matrix equation. To do so, we prove the existence of fixed points for multi-valued modified F -contractions in the context of complete metric spaces, which generalize, refine, and extend several existing results in the literature. An example is accompanies the obtained results to show that derived results are a proper generalization.

Suggested Citation

  • Nawab Hussain & Ghada Ali & Iram Iqbal & Bessem Samet, 2020. "The Existence of Solutions to Nonlinear Matrix Equations via Fixed Points of Multivalued F -Contractions," Mathematics, MDPI, vol. 8(2), pages 1-18, February.
    • Handle: RePEc:gam:jmathe:v:8:y:2020:i:2:p:212-:d:317815
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    References listed on IDEAS

    as
    1. Hemant Kumar Nashine & Zoran Kadelburg & Zorana Golubović, 2012. "Common Fixed Point Results Using Generalized Altering Distances on Orbitally Complete Ordered Metric Spaces," Journal of Applied Mathematics, Hindawi, vol. 2012, pages 1-12, May.
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    Cited by:

    1. Wei-Shih Du & Chung-Chuan Chen & Marko Kostić & Bessem Samet, 2023. "Preface to the Special Issue “Fixed Point Theory and Dynamical Systems with Applications”," Mathematics, MDPI, vol. 11(13), pages 1-2, June.

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