On the best areas for Kannan system and Chatterjea system in b-metric spaces. (3rd June 2021) - Lu, Ning; He, Fei; Du, Wei-Shih
Abstract : In this paper, we introduce the new concepts of the best area of Banach system, Kannan system and Chatterjea system with degree s in b -metric spaces with constant s . We prove that the best area for Kannan-type system with degree s is 0, min 1 2, 1 / s and the best area for Chatterjea-type system with degree s is 0, 1 2 in the setting of b -metric spaces with constant s . Moreover, we prove a generalization of Chatterjea-type fixed point theorem with the contraction constant λ ∈ [ 0, 1 ) in b -metric spaces which generalizes known results related with Chatterjea-type mapping in the existing literature. Finally, an example is given to illustrate our results.