Sbornik. Mathematics, Tome 13 (1971) no. 3, pp. 473-490
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A. P. Bulanov. Rational approximations to convex functions with given modulus of continuity. Sbornik. Mathematics, Tome 13 (1971) no. 3, pp. 473-490. http://geodesic.mathdoc.fr/item/SM_1971_13_3_a8/
@article{SM_1971_13_3_a8,
author = {A. P. Bulanov},
title = {Rational approximations to convex functions with given modulus of con\-tinuity},
journal = {Sbornik. Mathematics},
pages = {473--490},
year = {1971},
volume = {13},
number = {3},
language = {en},
url = {http://geodesic.mathdoc.fr/item/SM_1971_13_3_a8/}
}
TY - JOUR
AU - A. P. Bulanov
TI - Rational approximations to convex functions with given modulus of continuity
JO - Sbornik. Mathematics
PY - 1971
SP - 473
EP - 490
VL - 13
IS - 3
UR - http://geodesic.mathdoc.fr/item/SM_1971_13_3_a8/
LA - en
ID - SM_1971_13_3_a8
ER -
%0 Journal Article
%A A. P. Bulanov
%T Rational approximations to convex functions with given modulus of continuity
%J Sbornik. Mathematics
%D 1971
%P 473-490
%V 13
%N 3
%U http://geodesic.mathdoc.fr/item/SM_1971_13_3_a8/
%G en
%F SM_1971_13_3_a8
It is shown that for any convex continuous functions $f(x)$ ($x\in[a,b]$, $-\infty) with modulus of continuity $\omega(\delta)$ the order of approximation by rational functions does not exceed $$ C\cdot\frac{\ln^2n}n\cdot\inf_{0<\lambda<1}\biggl\{\omega(\lambda)+M\cdot\frac{\ln^2n}n\cdot\ln\frac{b-a}\lambda\biggr\}, $$ where $C$ is an absolute constant and $M=\max|f(x)|$. Bibliography: 6 titles.
[1] A. P. Bulanov, “O poryadke priblizheniya vypuklykh funktsii ratsionalnymi funktsiyami”, Izv. AN SSSR, seriya matem., 33 (1969), 1132–1148 | MR | Zbl
[2] P. Szusz, P. Turan, “On the constractive theory of function”, Magyar Tud. Acad. Mat. Kutato Int. Kozl., 1 (1965), 495–502 | MR
[3] A. P. Bulanov, “O nailuchshikh ratsionalnykh priblizheniyakh vypuklykh funktsiyu i funktsii s konechnym izmeneniem”, DAN SSSR, 190:1 (1970), 13–14 | MR | Zbl
