On the Conditions of Fixed-Point Theorems Concerning F-Contractions

• Published in: Resultate der Mathematik Vol. 73; no. 2
• Main Authors: Kajántó, Sándor, Lukács, Andor
• Format: Journal Article
• Language: English
• Published: Cham Springer International Publishing 01-06-2018
• Subjects: Mathematics; Mathematics and Statistics; Primary 47H09; 47H10; metric spaces; fixed-point theorems; contractions
• ISSN: 1422-6383; 1420-9012
• DOI: 10.1007/s00025-018-0846-1

We prove a fixed-point theorem that generalizes and simplifies a number of results in the theory of
F
-contractions. We show that all of the previously imposed conditions on the operator can be either omitted or relaxed. Furthermore, our result is formulated in the more general context of
b
-metric spaces and
φ
-contractions. We also point out that the framework of
F
-contractions can be reformulated in an equivalent way that is both closer in spirit to the classical syntax of Banach-type fixed point theorems, and also more natural and easier to deal with in the proofs.