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Banach’s fixed point theorem, Ćirić’s and Kannan’s are equivalent via redefining the metric
Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A. Matemáticas ( IF 2.9 ) Pub Date : 2020-07-10 , DOI: 10.1007/s13398-020-00897-1
Jenjira Puiwong , Satit Saejung

In the literature, the three fixed point theorems due to Banach, Kannan, and Ciric were proved independently. In this paper, we show that these three theorems are equivalent in the sense that any two of them can be deduced from the third one. Using the same technique, we show that two fixed point theorems proposed by Bessenyei can be deduced from Banach’s and Matkowski’s results.

中文翻译:

Banach 不动点定理,Ćirić's 和 Kannan's 通过重新定义度量等价

在文献中,由于 Banach、Kannan 和 Ciric 的三个不动点定理被独立证明。在本文中,我们证明这三个定理是等价的,因为它们中的任何两个都可以从第三个推导出来。使用相同的技术,我们表明可以从 Banach 和 Matkowski 的结果推导出 Besenyei 提出的两个不动点定理。
更新日期:2020-07-10
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