**Volume 10, Issue 8, pp 4162--4174**

**Publication Date**: 2017-08-11

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

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.

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.

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

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