TY - JOUR
AU - Voloshyn, H.A.
AU - Maslyuchenko, V.K.
PY - 2010/06/30
Y2 - 2024/06/25
TI - On approximation of the separately continuous functions $2\pi$-periodical in relation to the second variable
JF - Carpathian Mathematical Publications
JA - Carpathian Math. Publ.
VL - 2
IS - 1
SE - Scientific articles
DO -
UR - https://journals.pnu.edu.ua/index.php/cmp/article/view/3975
SP - 4-14
AB - <p>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 $x\in X$.</p>
ER -