Abstract
The aim of this manuscript is to establish fixed point results satisfying contractive conditions of rational type in the setting of b-metric spaces. The results proved herein are the generalization and extension of some well known results in the existing literature. Example is also given in order to illustrate the validity of the presented results.
Highlights
Introduction and PreliminariesThe Banach contraction principle [2] is considered to be the pioneering result of the fixed point theory, and plays an important role for solving existence problems in many branches of nonlinear analysis
For all x, y ∈ X with λ ∈ [0, 1), K has a unique fixed point. This principle have been improved and extended by several mathematicians in different directions some of them are as follows: Let K be a mapping on a metric space (X, d) and x, y ∈ X, K is said to be Received 2018-06-11; accepted 2018-08-13; published 2018-11-02. 2010 Mathematics Subject Classification
Several papers has been studied by many authors dealing with the existence of fixed point in b–metric spaces. The aim of this contribution is to investigate some fixed point results using the concept of the contractive conditions of rational type in the context of b–metric spaces
Summary
Introduction and PreliminariesThe Banach contraction principle [2] is considered to be the pioneering result of the fixed point theory, and plays an important role for solving existence problems in many branches of nonlinear analysis. The aim of this manuscript is to establish fixed point results satisfying contractive conditions of rational type in the setting of b-metric spaces.
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