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arXiv · 2507.03606

On the connections between $F$-contractions and Meir-Keeler contractions

Laura Manolescu·Pasc Gavruta
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Abstract

In this paper, we resolve an open problem concerning the connection between $F$-contractions (Wardowski contractions) and Meir-Keeler contractions. We prove that for a nondecreasing function $F$ that has a point of discontinuity on the right, there exists an $F-$contraction that is not a Meir-Keeler contraction. Moreover, we give a condition on nonlinear $(\varphi,F)$-contractions to be Meir-Keeler contractions. In the final part of the paper, we give a class of $(E,F)-$contractions (in the sense of the paper arXiv:2009.13157 [math.FA] 28 Sep 2020) that are Meir-Keeler contractions.

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Laura Manolescu, Pasc Gavruta. 2025-07-04. On the connections between $F$-contractions and Meir-Keeler contractions. https://arxiv.org/abs/2507.03606

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