On the weakest conditions for the existence of fixed points of Kannan and Chatterjea type contractions
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arXiv
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| Format: | Preprint |
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2025
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| author | Hashimoto, Shunya Kikkawa, Misako Machihara, Shuji Saghir, Aqib |
| author_facet | Hashimoto, Shunya Kikkawa, Misako Machihara, Shuji Saghir, Aqib |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2505_01672 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | On the weakest conditions for the existence of fixed points of Kannan and Chatterjea type contractions Hashimoto, Shunya Kikkawa, Misako Machihara, Shuji Saghir, Aqib Functional Analysis 54H25, 47H10 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. |
| title | On the weakest conditions for the existence of fixed points of Kannan and Chatterjea type contractions |
| topic | Functional Analysis 54H25, 47H10 |
| url | https://arxiv.org/abs/2505.01672 |