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arXiv · 1709.08419

On the conditions of fixed-point theorems concerning $F$-contractions

Sándor Kajántó·Andor Lukács
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Abstract

We prove a fixed-point theorem that generalises 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 $\varphi$-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.

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BibTeXRIS

Sándor Kajántó, Andor Lukács. 2017-09-25. On the conditions of fixed-point theorems concerning $F$-contractions. https://doi.org/10.1007/s00025-018-0846-1

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