(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.