Bui T. N. Han, Nguyen T. Hieu

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The purpose of this paper is to introduce the notion of a generalized cyclic contractive mapping in $b$-metric~spaces by adding four terms $\cfrac{d(T^2x,x)+d(T^2x,Ty)}{2s}$, $d(T^2x,Tx)$, $d(T^2x,y)$, $d(T^2x,Ty)$ and state a fixed point theorem for this kind of mappings. Also, some corollaries are derived from this theorem. In addition, some examples are given to illustrate the obtained results.


fixed point, b-metric space, generalized cyclic contractive mappings


fixed point; $b$-metric space; generalized cyclic contractive mappings

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