Best proximity results for cyclic α-implicit contractions in quasi-metric spaces and its consequences

Abstract

Beforehand we set up the new concept of cyclic α-implicit contractions and subsequently find best proximity points for such type of mappings on quasi-metric spaces and partially ordered quasi-metric spaces. Besides, we construct an example and deduce several related results to demonstrate the usability of our derived theorem. As a consequence of this study, we deliver a fixed point result and also a result on the existence of solution of a type of integral equation. Additionally, we point out some mistakes in a recent paper by Aydi et al. [Nonlinear Anal. Model. Control 21 (2016), no. 1, 40-56].