$(F,varphi ,alpha )_{s}$-contractions in $b$-metric spaces and applications
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Abstract:
In this paper, we introduce more general contractions called $varphi $-fixed point point for $(F,varphi ,alpha )_{s}$ and $(F,varphi ,alpha )_{s}$-weak contractions. We prove the existence and uniqueness of $varphi $-fixed point point for $(F,varphi ,alpha )_{s}$ and $(F,varphi ,alpha)_{s}$-weak contractions in complete $b$-metric spaces. Some examples are supplied to support the usability of our results. As applications, necessary conditions to ensure the existence of a unique solution for a nonlinear inequality problem are also discussed. Also, some new fixed point results in partial metric spaces are proved.
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Journal title
volume 08 issue 03
pages 173- 182
publication date 2019-08-01
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