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

‎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.