Hahnís pairs and zero inverse problem (in Ukrainian)

Author
V. K. Maslyuchenko, V. S. Melínyk, H. A. Voloshyn
Chernivtsi National University, Chernivtsi, Ukraine
Abstract
We prove that for a function $\alpha_0\colon [0,1] \rightarrow \mathbb{R}$ there exists a separately continuous function $f\colon [0,1]^{2} \rightarrow \mathbb{R}$ such that $E_{0}(f^{x})=\alpha_0(x)$ on [0,1] if and only if $\alpha_0$ is the nonnegative lower semicontinuous function, where $f^{x}(y)=f(x,y)$ for any $x, y, \in [0,1]$ and $E_{0}(g)$ is the best approximation of a function $g$ by a constant.
Keywords
inverse Bernsteinís theorem; Hahnís pair; separately continuous function
DOI
doi:10.15330/ms.48.1.74-81
Reference
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Pages
74-81
Volume
48
Issue
1
Year
2017
Journal
Matematychni Studii
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