Cyclic Generalized $\varphi$-Contractions in $b$-Metric Spaces and an Application to Integral Equations

Hemant Kumar Nashine, Zoran Kadelburg

We introduce the notion of cyclic generalized $\varphi$-contractive mappings in $b$-metric spaces and discuss the existence and uniqueness of fixed points for such mappings. Our results generalize many existing fixed point theorems in the literature. Examples are given to support the usability of our results. Finally, an application to existence problem for an integral equation is presented.