On Uniqueness of Fixed Points and Their Regularity

Diana Caponetti, Mieczysław Cichoń and Valeria Marraffa ()
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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

Mathematics, 2025, vol. 13, issue 18, 1-22

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.

Keywords: fixed point; seminorm; uniqueness; measure of noncompactness; fractional operator (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2025
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