Best proximity point for Z-contraction and suzuki type Z-contraction mappings with an application to fractional calculus

Abstract

In this article, we introduced the best proximity point theorems for Z-contraction and Suzuki type Z-contraction in the setting of complete metric spaces. Also by the help of weak P-property and P-property, we proved existence and uniqueness of best proximity point. There is a simple example toshowthe validityofour results. Ourresults extended and unify many existing results in the literature. Moreover, an application to fractional order functional differential equation is discussed.