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In this work, we introduce the \((\mathit{CLR})\)-property for the hybrid pairs of single-valued and multi-valued mappings and give some coincidence and common fixed point theorems for the hybrid pairs of some contractive conditions. Also, we will give some examples to illustrate the main results in this paper. Our results extend and improve some results given by some authors.

Common fixed point theorems for hybrid contractive pairs with the $(\mathit{CLR})$-property