Some new fixed point results in $\mathrm{b}$-metric space with rational generalized contractive condition

In this paper, we improve and generalize several results in fixed point theory to the $\mathrm{b}$-metric space. Where we confirm the existence of the fixed point for self mapping $T$ satisfying some rational contractive conditions. Over-more, we establish the uniqueness of the fixed point in some cases and give dynamic information linking the fixed points between them in the other cases. Some illustrative examples are furnished, which demonstrate the validity of the hypotheses.