Remarks on cyclic contractions in b-metric spaces and applications to integral equations

Abstract

In this note we construct counterexamples to answer open questions on cyclic contractions posed by Radenovic in (Afr Mat 27(1):291–295, 2016) and Radenovic et al. (Appl Math Comput 273:155–164, 2016), and to show an error in the result of Nashine et al. (Publ Inst Math (Beograd) (N.S.) 93(107):69–93, 2013). We also show that many applications of fixed point results in b-metric spaces to integral equations in the literature may be replaced by that in metric spaces.