Impact of Kannan Contraction on Khan Contraction and its Generalizations

Abstract

Several concepts of rational contractions originated during the last 50 years with vivid discussion on possible applications and practical examples. The main topic of this article is a Khan contraction, its modifications and generalizations, with the emphasis on its relation to some well-known classes of contractive mappings. We prove that a Khan contraction is an example of Bianchini and, consequently, a Ciric contraction. Further, some of its generalizations present a special type of Kannan contraction.