On linear interpolation of vector valued functions and its applications (in Ukrainian) 

Author 
vmaslyuchenko@gmail.com, galja.vlshin@gmail.com
Yuriy Fedkovych Chernivtsi National University; Bukovyna State University of Finance and Economics

Abstract 
We prove a theorem on the uniform and pointwise approximation of
a mapping $\varphi\colon [a,b]\rightarrow Z$ taking values in a
topological vector space by its linear interpolations. Using this
theorem we prove that if $Y$ is a compact space then every
separately continuous function $f\colon [a,b]\times Y\rightarrow
\mathbb{R}$ with at most countable projection of the discontinuity
point set $D(f)$ to $[a,b]$ belongs to the sequential closure of
the subspace of all continuous functions $g\colon [a,b]\times
Y\rightarrow \mathbb{R}$ in the space $S([a,b]\times Y)$ of all
separately continuous functions $f\colon [a,b]\times Y\rightarrow
\mathbb{R}$ with the topology of the layerwise uniform
convergence.

Keywords 
uniform and pointwise approximation; linear interpolations; separately continuous functions;
vector valued functions; sequential closure

Reference 
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Pages 
129133

Volume 
42

Issue 
2

Year 
2014

Journal 
Matematychni Studii

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