Strong b-Suprametric Spaces and Fixed Point Principles

In this paper, we introduce the strong b -suprametric spaces in which we prove the fixed point principles of Banach and Edelstein. Moreover, we prove a variational principle of Ekeland and deduce a Caristi fixed point theorem. Furthermore, we introduce the strong b -supranormed linear spaces in whic...

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Bibliographic Details
Published in:Complex analysis and operator theory 2024-09, Vol.18 (6), Article 148
Main Author: Berzig, Maher
Format: Article
Language:English
Subjects:
Analysis
Boundary value problems
Fixed points (mathematics)
Integral equations
Mathematics
Mathematics and Statistics
Operator Theory
Vector spaces
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Summary:In this paper, we introduce the strong b -suprametric spaces in which we prove the fixed point principles of Banach and Edelstein. Moreover, we prove a variational principle of Ekeland and deduce a Caristi fixed point theorem. Furthermore, we introduce the strong b -supranormed linear spaces in which we establish the fixed point principles of Brouwer and Schauder. As applications, we study the existence of solutions to an integral equation and to a third-order boundary value problem.
ISSN:1661-8254
1661-8262
DOI:10.1007/s11785-024-01594-2