Abstract
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 \(\varphi \)-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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Sándor Kajántó was supported by the Collegium Talentum 2017 Programme of Hungary.
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Kajántó, S., Lukács, A. On the Conditions of Fixed-Point Theorems Concerning \(\varvec{F}\)-Contractions. Results Math 73, 82 (2018). https://doi.org/10.1007/s00025-018-0846-1
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DOI: https://doi.org/10.1007/s00025-018-0846-1