Abstract
In this paper, we aim to obtain fixed-point results by merging the interesting fixed-point theorem of Pata and Suzuki in the framework of complete metric space and to extend these results by involving admissible mapping. After introducing two new contractions, we investigate the existence of a (common) fixed point in these new settings. In addition, we shall consider an integral equation as an application of obtained results.
Highlights
Introduction and PreliminariesFor the solution of several differential/fractional/integral equations, fixed-point theory plays a significant role
In the case of the inadequacy, the researcher in the fixed-point theory proposes some extension of the Banach contraction principle
We recall one of the significant theorems given by Popescu [1] inspired from the notion of C-condition defined by Suzuki [2]
Summary
For the solution of several differential/fractional/integral equations, fixed-point theory plays a significant role. In such investigations, usually well-known Banach fixed-point theorems are sufficient to provide the desired results. In the case of the inadequacy, the researcher in the fixed-point theory proposes some extension of the Banach contraction principle. We recall one of the significant theorems given by Popescu [1] inspired from the notion of C-condition defined by Suzuki [2]. Let T be a self-mapping on a metric space ( X, d). It is called C-condition if d(κ , T κ) ≤ d(κ , y) implies that d( T κ , Ty) ≤ d(κ , y), ∀κ , y ∈ X
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