Geodesic
The exact order of the best approximation to convex functions by~rational functions
Sbornik. Mathematics, Tome 32 (1977) no. 2, pp. 245-251

Voir la notice de l'article provenant de la source Math-Net.Ru

We show that the least uniform rational deviations $R_n(f)$ from the function $f(x)$, continuous and convex on the interval $[a,b]$, satisfy the condition $R_n(f)=o(1/n)$ as $n\to\infty$, and that $R_n(f)=O(1/n)$ uniformly for the continuous convex functions $f$ whose absolute values are bounded by unity. These estimates are precise with respect to the rate of decrease of the right-hand sides. Bibliography: 16 titles. 
@article{SM_1977_32_2_a4,
     author = {V. A. Popov and P. P. Petrushev},
     title = {The exact order of the best approximation to convex functions by~rational functions},
     journal = {Sbornik. Mathematics},
     pages = {245--251},
     publisher = {mathdoc},
     volume = {32},
     number = {2},
     year = {1977},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SM_1977_32_2_a4/}
}
TY  - JOUR
AU  - V. A. Popov
AU  - P. P. Petrushev
TI  - The exact order of the best approximation to convex functions by~rational functions
JO  - Sbornik. Mathematics
PY  - 1977
SP  - 245
EP  - 251
VL  - 32
IS  - 2
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/SM_1977_32_2_a4/
LA  - en
ID  - SM_1977_32_2_a4
ER  - 
%0 Journal Article
%A V. A. Popov
%A P. P. Petrushev
%T The exact order of the best approximation to convex functions by~rational functions
%J Sbornik. Mathematics
%D 1977
%P 245-251
%V 32
%N 2
%I mathdoc
%U http://geodesic.mathdoc.fr/item/SM_1977_32_2_a4/
%G en
%F SM_1977_32_2_a4
V. A. Popov; P. P. Petrushev. The exact order of the best approximation to convex functions by~rational functions. Sbornik. Mathematics, Tome 32 (1977) no. 2, pp. 245-251. http://geodesic.mathdoc.fr/item/SM_1977_32_2_a4/