On the best areas for Kannan system and Chatterjea system in b-metric spaces

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 $\left[0,min\left\{\frac{1}{2},1/s\right\}\right)$ and the best area for Chatterjea-type system with degree s is $\left[0,\frac{1}{2}\right)$ 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 $\lambda \in [0,1)$ 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.

Keywords:

• The best area of Kannan system
• the best area of Chatterjea system
• Kannan-type mapping
• Chatterjea-type mapping
• b-metric space

2010 MSC:

• 47H10
• 54H25

Disclosure statement

No potential conflict of interest was reported by the author(s).

Additional information

Funding

The second author was supported by the National Natural Science Foundation of China (11561049). The third author was supported by Grant No. MOST 107-2115-M-017-004-MY2 of the Ministry of Science and Technology of the Republic of China.