Abstract
Abstract In this paper, we prove the existence and uniqueness of a fixed point for some new classes of contractive mappings via α-admissible mappings in the framework of b-metric spaces. We also present an example to illustrate the usability of the obtained results. The generalized Ulam-Hyers stability and well-posedness of a fixed point equation via α-admissible mappings in b-metric spaces are given. MSC:46S40, 47S40, 47H10.
Highlights
1 Introduction and preliminaries 1.1 The b-metric space The Banach contraction mapping principle is the most important in mathematics analysis, it guarantees the existence and uniqueness of a fixed point for certain self-mapping in metric spaces and provides a constructive method to find this fixed point
In, Czerwik [ ] introduced b-metric spaces as a generalization of metric spaces and proved the contraction mapping principle in b-metric spaces that is an extension of the famous Banach contraction principle in metric spaces
We recall the definitions of the following class of (b)-comparison functions as given by Berinde [ ] in order to extend some fixed point results to the class of b-metric spaces
Summary
Introduction and preliminaries1.1 The b-metric space The Banach contraction mapping principle is the most important in mathematics analysis, it guarantees the existence and uniqueness of a fixed point for certain self-mapping in metric spaces and provides a constructive method to find this fixed point. A number of authors have investigated fixed point theorems in b-metric spaces (see [ – ] and the references therein). We recall the definitions of the following class of (b)-comparison functions as given by Berinde [ ] in order to extend some fixed point results to the class of b-metric spaces.
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