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Andor Lukács

Publications and source records attributed to Andor Lukács.

3 recordsLinked to original sources
arXiv2021

On possible generalisations of quasi-contractions

This paper investigates whether some fixed point theorems for quasi-contractions on metric spaces introduced by Cirìc in [1] and generalised by Kumam et al. in [2] can be improved further. It turns out that the answer is negative. We provide two examples of complete metric spaces and two operators without fixed points. We prove that for any possible straightforward relaxation of generalised quasi-contractive conditions, one of these operators satisfies the condition.

math.CA↗
arXiv2017

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

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 $φ$-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.

math.CA↗