A Caristi type fixed point theorem which characterizes metric completeness


Ravindra K Bisht




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