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arXiv:2505.01672 [math.FA]AbstractReferencesReviewsResources

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

Shunya Hashimoto, Misako Kikkawa, Shuji Machihara, Aqib Saghir

Published 2025-05-03Version 1

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 [7]. We show that the CJM condition is nearly the weakest possible to have a fixed point, and that a slight modification yields the weakest condition even for these two types of mappings.

Comments: 7 pages, no figures
Categories: math.FA
Subjects: 54H25, 47H10
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