# Some applications with new admissibility contractions in $b$-metric spaces

Volume 10, Issue 8, pp 4162--4174

Publication Date: 2017-08-11

http://dx.doi.org/10.22436/jnsa.010.08.12

### Authors

Ljiljana Paunović - University of Priˇstina-Kosovska Mitrovica, Teacher Education School in Prizren-Leposavi´c, 38218 Leposavi´c, Serbia.
Preeti Kaushik - Department of Mathematics, DCRUST, Murthal, Sonepat 131039, India.
Sanjay Kumar - Department of Mathematics, DCRUST, Murthal, Sonepat 131039, India.

### Abstract

The work presented in this paper extends the idea of $\alpha-\beta$-contractive mappings in the framework of $b$-metric spaces. Fixed points are investigated for such kind of mappings. An example is given to show the superiority of our results. As applications we discuss Ulam-Hyres stability, well-posedness and limit shadowing of fixed point problem.

### Keywords

$\alpha-\beta(b)$-admissible mappings, fixed point, $b$-metric space, stability.

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