### Extensions of Meir-Keeler Contraction via w-Distances with an Application

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**Authors:**S BAROOTKOOB, E. KARAPıNAR, H. LAKZIAN AND A. CHANDA

**DOI:**10.46793/KgJMat2204.533B

**Abstract:**

In this article, we conceive the notion of a generalized (α,ψ,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.

**Keywords:**

w-distance, α-orbital admissible map, weaker Meir-Keeler function, Fredholm integral equation.

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