Abstract
In this paper, we extend the concept of contraction mappings in b-metric spaces and utilize this concept to prove the existence and uniqueness of fixed point theorems for such mappings in such a space. We also prove the generalized Ulam-Hyers stability and well-posed results for a fixed point equation employing the concept of α-admissibility in b-metric spaces. We shall construct some examples to support our novel results.MSC:46S40, 47S40, 47H10.
Highlights
The classical Banach contraction principle is a very important tool in solving existence problems in many branches of mathematics
A large number of papers have been published in connection with various generalizations of Ulam-Hyers stability results in fixed point theory and remarkable result on the stability of certain classes of functional equations via fixed point approach
We extend the concept of α-ψ-contractive mapping in b-metric spaces
Summary
The classical Banach contraction principle is a very important tool in solving existence problems in many branches of mathematics. Several other authors [ – ] have studied and established the existence of fixed points of a contractive mapping in b-metric spaces. They proved some fixed point results for such mappings in complete metric spaces.
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