English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Tools annual

Global: Zendy Free Plan

Global: Zendy Tools monthly

Global: Zendy Plus monthly

In this paper we obtain a generalization of Matkowski’s fixed point theorem and Istrăţescu’s fixed point theorem concerning convex contractions. More precisely, given a complete b-metric space (X, d) we prove that every continuous function \( f:X\rightarrow X\) is a Picard operator, provided that there exist \( m\in \mathbb {N}^{*}\) and a comparison function \(\varphi \) such that \(d(f^{[m]}(x),f^{[m]}(y))\le \varphi (\max \{d(x,y),d(f(x),f(y)),\ldots ,d(f^{[m-1]}(x),f^{[m-1]}(y))\})\) for all \(x,y\in X\). In addition, we point out that if \(m=1\), taking into account that a metric space is a b-metric space, we obtain a generalization of Matkowski’s fixed point theorem. Moreover, we prove that Istrăţescu’s fixed point theorem concerning convex contractions is a particular case of our result for \(m=2\). By providing appropriate examples we show that the above-mentioned two generalizations are effective.

A generalization of Matkowski’s fixed point theorem and Istrăţescu’s fixed point theorem concerning convex contractions