Some results of coincidence points on $b$-metric space

In this paper, we extend some results of a coincidence point for mappings $\psi$, $\varphi$ acting from a metric space to another one — to a space with a generalized distance. In our case, mappings $\psi$, $\varphi$ are acting from $b$-metric space to a space with a generalized distance (distance satisfying only the axiom of identity, i.e., symmetry and triangle inequality are not satisfied). The mapping $\psi$ is $\alpha$-covering and $\varphi$ is $\beta$-Lipschitz. Also, we study the stability of a coincidence point for mappings $\psi$, $\varphi$. We obtain the convergence of a coincidence point for mappings $\psi_n$, $\varphi_n$ to a coincidence point for mappings $\psi$, $\varphi$ when we have some convergence $\psi_n$ to $\psi$ and $\varphi_n$ to $\varphi$ as $n\to \infty$.