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

Voir la notice de l'article provenant de la source Math-Net.Ru

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 
@article{JSFU_2025_18_1_a11,
     author = {Hossein Lakzian and Sedigheh Barootkoob and Nicola Fabiano and Stojan Radenovi\'c},
     title = {On weakly contractions via $w$-distances},
     journal = {\v{Z}urnal Sibirskogo federalʹnogo universiteta. Matematika i fizika},
     pages = {109--118},
     publisher = {mathdoc},
     volume = {18},
     number = {1},
     year = {2025},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/JSFU_2025_18_1_a11/}
}
TY  - JOUR
AU  - Hossein Lakzian
AU  - Sedigheh Barootkoob
AU  - Nicola Fabiano
AU  - Stojan Radenović
TI  - On weakly contractions via $w$-distances
JO  - Žurnal Sibirskogo federalʹnogo universiteta. Matematika i fizika
PY  - 2025
SP  - 109
EP  - 118
VL  - 18
IS  - 1
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/JSFU_2025_18_1_a11/
LA  - en
ID  - JSFU_2025_18_1_a11
ER  - 
%0 Journal Article
%A Hossein Lakzian
%A Sedigheh Barootkoob
%A Nicola Fabiano
%A Stojan Radenović
%T On weakly contractions via $w$-distances
%J Žurnal Sibirskogo federalʹnogo universiteta. Matematika i fizika
%D 2025
%P 109-118
%V 18
%N 1
%I mathdoc
%U http://geodesic.mathdoc.fr/item/JSFU_2025_18_1_a11/
%G en
%F JSFU_2025_18_1_a11
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/

[1] N.Fabiano, Z.Kadelburg, N.Mirkov, V. Šešum Č avić, S.Radenović, “On F-contractions: A Survey”, Contamporary Mathematics, 3, no. 3, 2022, 327 | DOI

[2] O.Kada, T.Suzuki, W.Takahashi, “Nonconvex minimization theorems and fixed point theorems in complete metric spaces”, Math. Japonica, 44:2 (1996), 381–391 | MR | Zbl

[3] Z.Kadelburg, S.Radenović, “Some new observations on w-distance and F-contractions”, Matematički Vesnik (to appear) | MR

[4] R.Kannan, “Some results on fixed points II”, Am. Math. Mon., 76 (1969), 405–408 | MR | Zbl

[5] E.Karapinar, “Revisiting the Kannan type contractions via interpolation”, Advances in the Theory of Nonlinear Analysis and its Applications, 2:2 (2018), 85–87 | DOI | Zbl

[6] S.Radenović, Z.Kadelburg, D.Jandrlić, A.Jandrlić, “Some results on weakly contractive maps”, Bulletin of the Iranian Mathematical Society, 38:3 (2012), 625–645 | MR | Zbl

[7] T.Suzuki, “Several fixed point theorems in complete metric spaces”, Yokohama Mathematical Journal, 44 (1997), 61–72 | MR | Zbl

[8] D.Wardowski, “Fixed points of a new type of contractive mappings in complete metric spaces”, Fixed Point Theory Appl., 2012 (2012), 94 | DOI | MR | Zbl