A note on some recent fixed point results for cyclic contractions in b-metric spaces and an application to integral equations

In this paper we obtain some equivalences between cyclic contractions and non-cyclic contractions in the framework of b-metric spaces. Our results improve and complement several recent fixed point results for cyclic contractions in b -metric spaces established by George et al. (2015) and Nashine et al. (2014). Moreover, all the results are with much shorter proofs. In addition, an application to integral equations is given to illustrate the usability of the obtained results.