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Approximating Solutions of Matrix Equations via Fixed Point Techniques

Author

Listed:
  • Rahul Shukla

    (Department of Mathematics & Applied Mathematics, University of Johannesburg, Kingsway Campus, Auckland Park 2006, South Africa
    All authors contributed equally to this work.)

  • Rajendra Pant

    (Department of Mathematics & Applied Mathematics, University of Johannesburg, Kingsway Campus, Auckland Park 2006, South Africa
    All authors contributed equally to this work.)

  • Hemant Kumar Nashine

    (Department of Mathematics & Applied Mathematics, University of Johannesburg, Kingsway Campus, Auckland Park 2006, South Africa
    Department of Mathematics, Vellore Institute of Technology, School of Advanced Sciences, Vellore 632014, Tamil Nadu, India
    All authors contributed equally to this work.)

  • Manuel De la Sen

    (Faculty of Science and Technology, Institute of Research and Development of Processes IIDP, University of the Basque Country, Barrio Sarriena, 48940 Leioa, Bizkaia, Spain
    All authors contributed equally to this work.)

Abstract

The principal goal of this work is to investigate new sufficient conditions for the existence and convergence of positive definite solutions to certain classes of matrix equations. Under specific assumptions, the basic tool in our study is a monotone mapping, which admits a unique fixed point in the setting of a partially ordered Banach space. To estimate solutions to these matrix equations, we use the Krasnosel’skiĭ iterative technique. We also discuss some useful examples to illustrate our results.

Suggested Citation

  • Rahul Shukla & Rajendra Pant & Hemant Kumar Nashine & Manuel De la Sen, 2021. "Approximating Solutions of Matrix Equations via Fixed Point Techniques," Mathematics, MDPI, vol. 9(21), pages 1-16, October.
    • Handle: RePEc:gam:jmathe:v:9:y:2021:i:21:p:2684-:d:662540
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