# On approximation of the separately continuous functions $2\pi$-periodical in relation to the second variable

## Keywords:

separately continuous function, Jackson's operator, Bernstein's operator
Published online:
2010-06-30

### Abstract

Using Jackson's and Bernstein's operators we prove that for every topological space $X$ and an arbitrary separately continuous function $f: X \times \mathbb{R}\rightarrow \mathbb{R}$, $2\pi$-periodical in relation to the second variable, there exists such sequence of jointly continuous functions $f_n: X \times \mathbb{R}\rightarrow \mathbb{R}$ such that functions $f_n^x=f_n(x, \cdot): \mathbb{R}\rightarrow \mathbb{R}$ are trigonometric polynomials and $f_n^x\rightrightarrows f^x$ on $\mathbb{R}$ for every $x\in X$.

How to Cite

(1)

Voloshyn, H.; Maslyuchenko, V. On Approximation of the Separately Continuous Functions $2\pi$-Periodical in Relation to the Second Variable.

*Carpathian Math. Publ.***2010**,*2*, 4-14.