Cyclic Generalized $\varphi$-contractions in $b$-metric Spaces and an Application to Integral Equations

Abstract

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.