The weakest condition for a Kannan-type contraction mapping on a complete metric space

Abstract: In this paper, we investigate the weakest possible conditions for fixed point theorems concerning two types of mappings: Kannan and Chatterjea. We employ the so-called CJM condition, which has been successfully applied to the classical Banach-type mappings by \'Ciri\'c [5]. We show that the CJM condition is nearly the weakest possible to have a fixed point even for these two types of mappings, and that those slight modifications yield the weakest condition.