Best proximity point theorems for $ \alpha^{+} F, (\theta-\phi )$-proximal contraction

In this paper, inspired by the idea of Suzuki type $ \alpha^{+} F$-proximal contraction in metric spaces, we prove a new existence of best proximity point for Suzuki type $ \alpha^{+} F$-proximal contraction and $ \alpha^{+} (\theta-\phi )$-proximal contraction defined on a closed subset of a complete metric space. Our theorems extend, generalize, and improve many existing results.