On some generalized contractive maps in partial metric space and related fixed point theorems

Abstract

In this paper we generalize some results of fixed point theory to partial metric spaces by using metric methods in the context of a new extension of Ekeland’s variational principle. We provide some
corollaries to unify our results with other existing results in the literature along the same vein. Then, we show that our results require existence assumptions weaker than those for some well-known contractive
maps, including the ones in the sense of Banach, Ciric, Song, Kannan and Hardy Rogers. Also, we provide some estimates for the distance to the fixed point set in partial metric space. In order to illustrate the
strength of our fixed point theorem, we use it in order to derive a new result on coupled fixed points.