BEST PROXIMITY AND FIXED POINT OUTCOMES IN METRIC SPACES FOR THE PROXIMAL CONTRACTION OF $\alpha_{0}-(\psi_0, g_0)$

In this paper, we introduce new notions of $\alpha_{0}-(\psi_0, g_0)$ - proximal contraction of Type-I and Type-II and modified $\alpha_{0}-(\psi_0, g_0)$ - proximal contraction. In the setting of these notions, we prove certain fixed point theorems in metric space. Additionally, a few applications are provided to show how the results can be used.