$(F,\varphi‎ ,‎\alpha )_{s}$-contractions in ‎$‎b‎$‎-metric spaces and applications

Journal of Linear and Topological Algebra

مقاله 3، دوره 08، شماره 03، آبان 2019، صفحه 173-182   

نوع مقاله: Research Paper

نویسنده

M. Sangurlu Sezen^*

Department of Mathematics‎, ‎Faculty of Science and Arts‎, ‎Giresun University‎, ‎Turkey

چکیده

‎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.

کلیدواژه‌ها

$b$-metric space؛ ‎partial $b$-metric space‎؛ ‎$(F,varphi‎,‎alpha )_{s}$-contraction‎؛ ‎$varphi$-fixed point

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