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arXiv · 2505.01672

On the weakest conditions for the existence of fixed points of Kannan and Chatterjea type contractions

Shunya Hashimoto·Misako Kikkawa·Shuji Machihara·Aqib Saghir
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Abstract

In this paper, we study the weakest possible conditions for fixed point theorems involving two classes of mappings defined by Kannan and Chatterjea. Our approach relies on the so-called CJM condition, which was originally introduced by \'Ciri\'c [5], and later, Suzuki [18] showed that the CJM condition is necessary for the existence of fixed points and the convergence of all Picard sequences of Banach type mappings. Our aim is to extend Suzuki's approach to the case of Kannan and Chatterjea mappings. In particular, in the first case, we discuss the equivalence of previously known conditions and establish that our conditions are optimal for ensuring that all Picard sequences converge to a fixed point of a mapping.

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Shunya Hashimoto, Misako Kikkawa, Shuji Machihara, Aqib Saghir. 2025-05-03. On the weakest conditions for the existence of fixed points of Kannan and Chatterjea type contractions. https://arxiv.org/abs/2505.01672

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