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On the best areas for Kannan system and Chatterjea system in \(b\)-metric spaces. (English) Zbl 1481.54050

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

MSC:

54H25 Fixed-point and coincidence theorems (topological aspects)
54E40 Special maps on metric spaces
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References:

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