On the best areas for Kannan system and Chatterjea system in b-metric spaces. (3rd June 2021)

• Record Type: Journal Article
• Authors: Lu, Ning; He, Fei; Du, Wei-Shih
• Is Part Of: Optimization. Volume 70:Number 5/6(2021)
• Page Start: 973
• Page End: 986
• Publication Date: 2021-06-03
• Subjects: The best area of Kannan system -- the best area of Chatterjea system -- Kannan-type mapping -- Chatterjea-type mapping -- b-metric space; 47H10 -- 54H25; Mathematical optimization -- Periodicals; 519.7
• DOI: 10.1080/02331934.2020.1727902
• Languages: English
• ISSNs: 0233-1934

Abstract

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.