- Advances in the Theory of Nonlinear Analysis and its Application
- Vol: 6 Issue: 4
- Hu's characterization of metric completeness revisited
Hu's characterization of metric completeness revisited
Authors : Salvador ROMAGUERA BONİLLA
Pages : 476-480
Doi:10.31197/atnaa.1090077
View : 6 | Download : 1
Publication Date : 2022-12-30
Article Type : Research
Abstract :In this note we show the somewhat surprising fact that the proof of the `if part\' of the distinguished characterizations of metric completeness due to Kirk, and Suzuki and Takahashi, respectively, can be deduced in a straightforward manner from Hu\'s theorem that a metric space is complete if and only if any Banach contraction on bounded and closed subsets thereof has a fixed point. We also take advantage of this approach to easily deduce a characterization of metric completeness via fixed point theorems for $\\alpha -\\psi $-contractive mappings.Keywords : Fixed point, , complete metric space, Hu, Caristi-Kirk, Suzuki-Takahashi