Extensions of Meir-Keeler Contraction via $w$-distances with an Application

Sedigheh Barootkoob, Erdal Karapinar, Hosein Lakzian, Ankush Chanda

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.