Certain positive linear operators
Matematičeskie zametki, Tome 23 (1978) no. 5, pp. 659-669
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Properties (including the approximating ones) are investigated of positive linear operators $L_n(f; x)$ for which the relation $$ L_n((t-x)f(t);x)=\frac{\varphi(x)}{n}L_n'(f(t); x) $$ is fulfilled, as well as the properties of operators $L_n^{(m)}(f; x)$. The results are applicable, in particular, to Bernstein polynomials, to the operators of Mirak'yan, Baskakov, and others.
@article{MZM_1978_23_5_a2,
author = {Yu. I. Volkov},
title = {Certain positive linear operators},
journal = {Matemati\v{c}eskie zametki},
pages = {659--669},
year = {1978},
volume = {23},
number = {5},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/MZM_1978_23_5_a2/}
}
Yu. I. Volkov. Certain positive linear operators. Matematičeskie zametki, Tome 23 (1978) no. 5, pp. 659-669. http://geodesic.mathdoc.fr/item/MZM_1978_23_5_a2/