On possible generalisations of quasi-contractions

2021/03/23 by Tünde Cseh, Cseh, Tünde, Sándor Kajántó +3
Mathematics · #47H10 #54H25 #Classical Analysis and ODEs (math.CA) #FOS: Mathematics #Fixed Point Theorems Analysis #General Topology (math.GN)

paper · pdf · doi:10.48550/arxiv.2103.12485

openalex publication_date 2021/03/23 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

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.

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