2025/05/03 by Shunya Hashimoto, Hashimoto, Shunya, Misako Kikkawa +5
Mathematics · Physics and Astronomy · #Fixed Point Theorems Analysis #Advanced Differential Geometry Research
paper · pdf · doi:10.48550/arxiv.2505.01672
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 Ćirić [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.