‎In this paper‎, ‎we introduce more general contractions called $\varphi $-fixed‎‎point 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 are‎‎supplied to support the usability of our results‎. ‎As applications‎, ‎necessary‎‎conditions to ensure the existence of a unique solution for a nonlinear‎‎inequality problem are also discussed‎. ‎Also‎, ‎some new fixed point results in‎‎partial metric spaces are proved. تفاصيل المقالة

In this paper, we prove the existence and uniqueness of fixed points for cyclic (α,β)-admissible type F-contraction and F−weak contraction under the setting of modular spaces, where the modular is convex and satisfying the ∆2-condition. Later, we prove some periodic point results for self-mappings on a modular space. We also give some examples to support our results. تفاصيل المقالة