Geodesic
On weakly contractions via $w$-distances
Žurnal Sibirskogo federalʹnogo universiteta. Matematika i fizika, Tome 18 (2025) no. 1, pp. 109-118

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In this article, we will check whether the known results remain valid if the metric $d$ is replaced by the $w$ -distance $p$. we show that in some contractive conditions where $w$-distance $p$ participates instead of metric $d$, symmetry of $w$-distance $p$ can be assumed and the proofs can be shorter. We are talking about results such as Banach's contraction principle, Kannan's theorem, Boyd–Wong, Meir–Keeler, Chatterje's, Reich's, Hardy–Rogers', Karapinars' and Wardowskis' theorems and many others. By doing so, we would obtain generalizations of the above results.
Keywords: fixed point, $w$-distance, $p$-Hardy–Rogers contraction, $(\digamma,p)$-contraction.
Mots-clés : $p$-interpolative Kannan type contraction 
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Hossein Lakzian; Sedigheh Barootkoob; Nicola Fabiano; Stojan Radenović. On weakly contractions via $w$-distances. Žurnal Sibirskogo federalʹnogo universiteta. Matematika i fizika, Tome 18 (2025) no. 1, pp. 109-118. http://geodesic.mathdoc.fr/item/JSFU_2025_18_1_a11/