Some Unique Fixed Point Theorems on Complete Metric Space with Upper Semi Continuous Mapping

Abstract

In the present article, we have proved two common fixed point theorems (FPT) for complete metric space (CMS) with the help of upper semi-continuous function along with the existence and uniqueness of fixed point. These results are the  generalizations of the well-known theorems Kannan fixed point theorem (KFPT) and Chatterjea fixed point theorem (CFPT) in the existed literature. The KFPT and CFPT are the generalizations of Banach fixed point theorem (BFPT).