A Caristi type fixed point theorem which characterizes metric completness

Abstract

In this paper, we improve Caristi-Jachymski-SteinJr and Banach-Caristi type fixed point theorems by relaxing strong continuity assumption of the mapping by some weaker continuity notions. As an application, we show that the weaker version of Caristi-Jachymski-SteinJr type fixed point theorem characterizes the completeness of the metric space and the Cantor intersection property.