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A Generalization of Fixed-Point Theorems for Mappings with a Contractive Iterate

Author

Listed:
  • Valentin Georgiev

    (Department of Mathematical Analysis, Faculty of Mathematics and Informatics, University of Plovdiv Paisii Hilendarski, 24 “Tzar Assen” Str., 4000 Plovdiv, Bulgaria
    These authors contributed equally to this work.)

  • Boyan Zlatanov

    (Department of Mathematical Analysis, Faculty of Mathematics and Informatics, University of Plovdiv Paisii Hilendarski, 24 “Tzar Assen” Str., 4000 Plovdiv, Bulgaria
    These authors contributed equally to this work.)

Abstract

In this paper, a generalization of fixed-point mappings with an iterate at a point in complete metric spaces is shown, using the notions of T-closed sets and i-P-regularity/d-P-regularity, proving conditions for the existence and uniqueness of the fixed point. Examples are provided to illustrate the results and an application to coupled fixed points is shown.

Suggested Citation

  • Valentin Georgiev & Boyan Zlatanov, 2024. "A Generalization of Fixed-Point Theorems for Mappings with a Contractive Iterate," Mathematics, MDPI, vol. 12(23), pages 1-11, November.
    • Handle: RePEc:gam:jmathe:v:12:y:2024:i:23:p:3725-:d:1530977
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