On the connections between $F$-contractions and Meir-Keeler contractions
Laura Manolescu, Pasc Gavruta
TL;DR
This paper investigates the relationship between $F$-contractions and Meir-Keeler contractions, providing conditions under which they coincide or differ, and constructing specific examples to clarify their connections.
Contribution
It resolves an open problem by showing that certain $F$-contractions are not Meir-Keeler contractions and establishes criteria for nonlinear $( ,F)$-contractions to be Meir-Keeler contractions.
Findings
Existence of $F$-contractions that are not Meir-Keeler contractions.
Conditions under which $( ,F)$-contractions are Meir-Keeler contractions.
Identification of classes of $(E,F)$-contractions that are Meir-Keeler contractions.
Abstract
In this paper, we resolve an open problem concerning the connection between -contractions (Wardowski contractions) and Meir-Keeler contractions. We prove that for a nondecreasing function that has a point of discontinuity on the right, there exists an contraction that is not a Meir-Keeler contraction. Moreover, we give a condition on nonlinear -contractions to be Meir-Keeler contractions. In the final part of the paper, we give a class of contractions (in the sense of the paper arXiv:2009.13157 [math.FA] 28 Sep 2020) that are Meir-Keeler contractions.
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