(F, φ, α)s-contractions in b-metric spaces and applications

In this paper, we introduce more general contractions called φ-fixed point point for (F, φ, α)s and (F, φ, α)s-weak contractions. We prove the existence and uniqueness of φ- fixed point point for (F, φ, α)s and (F, φ, α)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.