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The Stability and Well-Posedness of Fixed Points for Relation-Theoretic Multi-Valued Maps

Author

Listed:
  • Isaac Karabo Letlhage

    (Department of Mathematics and Applied Mathematics, University of Johannesburg, Kingsway Campus, Auckland Park 2006, South Africa)

  • Deepak Khantwal

    (Department of Mathematics and Applied Mathematics, University of Johannesburg, Kingsway Campus, Auckland Park 2006, South Africa)

  • Rajendra Pant

    (Department of Mathematics and Applied Mathematics, University of Johannesburg, Kingsway Campus, Auckland Park 2006, South Africa)

  • Manuel De la Sen

    (Institute of Research and Development of Processes IIDP, Faculty of Science and Technology, University of the Basque Country, de Bilbao, Barrio Sarriena, 48940 Leioa, Bizkaia, Spain)

Abstract

The purpose of this study is to present fixed-point results for Suzuki-type multi-valued maps using relation theory. We examine a range of implications that arise from our primary discovery. Furthermore, we present two substantial cases that illustrate the importance of our main theorem. In addition, we examine the stability of fixed-point sets for multi-valued maps and the concept of well-posedness. We present an application to a specific functional equation which arises in dynamic programming.

Suggested Citation

  • Isaac Karabo Letlhage & Deepak Khantwal & Rajendra Pant & Manuel De la Sen, 2023. "The Stability and Well-Posedness of Fixed Points for Relation-Theoretic Multi-Valued Maps," Mathematics, MDPI, vol. 11(20), pages 1-13, October.
    • Handle: RePEc:gam:jmathe:v:11:y:2023:i:20:p:4271-:d:1259060
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    References listed on IDEAS

    as
    1. Mishra, S.N. & Singh, S.L. & Pant, Rajendra, 2012. "Some new results on stability of fixed points," Chaos, Solitons & Fractals, Elsevier, vol. 45(7), pages 1012-1016.
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