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On Uniqueness of Fixed Points and Their Regularity

Author

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  • Diana Caponetti

    (Dipartimento di Matematica e Informatica, Università di Palermo, 90123 Palermo, Italy)

  • Mieczysław Cichoń

    (Faculty of Mathematics and Computer Science, Adam Mickiewicz University, 61-614 Poznań, Poland)

  • Valeria Marraffa

    (Dipartimento di Matematica e Informatica, Università di Palermo, 90123 Palermo, Italy)

Abstract

In this paper, we study the problem of uniqueness of fixed points for operators acting from a Banach space X into a subspace Y with a stronger norm. Our main objective is to preserve the expected regularity of fixed points, as determined by the norm of Y , while analyzing their uniqueness without imposing the classical or generalized contraction condition on Y . The results presented here provide generalized uniqueness theorems that extend existing fixed-point theorems to a broader class of operators and function spaces. The results are used to study fractional initial value problems in generalized Hölder spaces.

Suggested Citation

  • Diana Caponetti & Mieczysław Cichoń & Valeria Marraffa, 2025. "On Uniqueness of Fixed Points and Their Regularity," Mathematics, MDPI, vol. 13(18), pages 1-22, September.
    • Handle: RePEc:gam:jmathe:v:13:y:2025:i:18:p:2996-:d:1750757
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