Work

On Uniqueness of Fixed Points and Their Regularity

Year: 2025

Type: article

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.

Source: Mathematics

DOI: 10.3390/math13182996

Authors: Diana Caponetti, Mieczysław Cichoń, Valeria Marraffa

Institutions: University of Palermo, Adam Mickiewicz University in Poznań

Language: English

Topic: Fixed Point Theorems Analysis

Subfield: Geometry and Topology

Field: Mathematics

Domain: Physical Sciences

Open Access status: gold

Estimated APC paid: $3,137

Funder: Università degli Studi di Palermo