Hu`s characterization of metric completeness revisited

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Advances in the Theory of Nonlinear Analysis and its Application
Volume: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 : 8 | Download : 9

Publication Date : 2022-12-30

Article Type : Research Paper

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

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