Best Proximity Points and Fixed Points Results for Noncyclic and Cyclic Fisher Quasi-contractions

Abstract

In this article, in the setting of metric spaces we introduce the notions of noncyclic and cyclic Fisher quasi-contraction mappings. We establish the existence of an optimal pair of fixed points for a noncyclic Fisher quasi-contraction mapping and iterative algorithms are furnished to determine such optimal pair of fixed points. For a cyclic Fisher quasi-contraction mapping, we also study the existence of best proximity points. Presented results extend and improve some recent results in the literature. © 2019, © 2019 Taylor & Francis Group, LLC.