Extensions of Meir-Keeler contraction via \(w\)-distances with an application. (English) Zbl 1524.54084
Summary: 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.
MSC:
| 54H25 | Fixed-point and coincidence theorems (topological aspects) |
| 54E40 | Special maps on metric spaces |
| 54E50 | Complete metric spaces |
| 45B05 | Fredholm integral equations |
| 45G10 | Other nonlinear integral equations |
Keywords:
\(w\)-distance; \(\alpha\)-orbital admissible map; weaker Meir-Keeler function; Fredholm integral equationReferences:
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