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

Author
Yuriy Fedkovych Chernivtsi National University; Bukovyna State University of Finance and Economics
Abstract
We prove a theorem on the uniform and point-wise 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 layer-wise uniform convergence.
Keywords
uniform and point-wise approximation; linear interpolations; separately continuous functions; vector valued functions; sequential closure
Reference
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Pages
129-133
Volume
42
Issue
2
Year
2014
Journal
Matematychni Studii
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