Geodesic
Extensions of Meir-Keeler Contraction via $w$-distances with an Application
Kragujevac Journal of Mathematics, Tome 46 (2022) no. 4, p. 533

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In this article, we conceive the notion of a generalized $(\alpha,\psi,q)$-Meir-Keeler contractive mapping and then we investigate a fixed point theorem involving such kind of contractions in the setting of a complete metric space via a $w$-distance. Our obtained result extends and generalizes some of the previously derived fixed point theorems in the literature via $w$-distances. In addition, to validate the novelty of our findings, we illustrate a couple of constructive numerical examples. Moreover, as an application, we employ the achieved result to earn the existence criteria of the solution of a kind of non-linear Fredholm integral equation.
Classification : 47H10 47H09, 54H25
Keywords: $w$-distance, $\alpha$-orbital admissible map, weaker Meir-Keeler function, Fredholm integral equation 
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     author = {Sedigheh Barootkoob and Erdal Karapinar and Hosein Lakzian and Ankush Chanda},
     title = {Extensions of {Meir-Keeler} {Contraction} via $w$-distances with an {Application}},
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Sedigheh Barootkoob; Erdal Karapinar; Hosein Lakzian; Ankush Chanda. Extensions of Meir-Keeler Contraction via $w$-distances with an Application. Kragujevac Journal of Mathematics, Tome 46 (2022) no. 4, p. 533 . http://geodesic.mathdoc.fr/item/KJM_2022_46_4_a2/