Geodesic
On the order of approximation of convex functions by rational functions
Izvestiya. Mathematics , Tome 3 (1969) no. 5, pp. 1067-1080.

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

We show that for arbitrary convex functions the order of approximation (in the metric $C[a,b]) by rational functions of degree no higher than $n$ does not exceed the quantity $C\cdot M\cdot\frac{\ln^2n}n$ ($C$ an absolute constant, $M$ the maximum modulus of the convex function). We prove also the existence of a~convex function whose order of approximation is greater than $\frac1{n\ln^2n}$. 
@article{IM2_1969_3_5_a7,
     author = {A. P. Bulanov},
     title = {On the order of approximation of convex functions by rational functions},
     journal = {Izvestiya. Mathematics },
     pages = {1067--1080},
     publisher = {mathdoc},
     volume = {3},
     number = {5},
     year = {1969},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/IM2_1969_3_5_a7/}
}
TY  - JOUR
AU  - A. P. Bulanov
TI  - On the order of approximation of convex functions by rational functions
JO  - Izvestiya. Mathematics 
PY  - 1969
SP  - 1067
EP  - 1080
VL  - 3
IS  - 5
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/IM2_1969_3_5_a7/
LA  - en
ID  - IM2_1969_3_5_a7
ER  - 
%0 Journal Article
%A A. P. Bulanov
%T On the order of approximation of convex functions by rational functions
%J Izvestiya. Mathematics 
%D 1969
%P 1067-1080
%V 3
%N 5
%I mathdoc
%U http://geodesic.mathdoc.fr/item/IM2_1969_3_5_a7/
%G en
%F IM2_1969_3_5_a7
A. P. Bulanov. On the order of approximation of convex functions by rational functions. Izvestiya. Mathematics , Tome 3 (1969) no. 5, pp. 1067-1080. http://geodesic.mathdoc.fr/item/IM2_1969_3_5_a7/

[1] Gonchar A. A., “O nailuchshikh priblizheniyakh ratsionalnymi funktsiyami”, Dokl. AN SSSR, 100:2 (1955), 205–208 | Zbl

[2] Dolzhenko E. P., “Skorost priblizheniya ratsionalnymi drobyami i svoistva funktsii”, Matem. sb., 56(98) (1962), 403–432 | Zbl

[3] Dolzhenko E. P., “Sravnenie skorostei ratsionalnoi i polinomialnoi approksimatsii”, Matem. zametki, 1:3 (1967), 313–320 | Zbl

[4] Szüsz P., Turan P., “On the constructive theory of functions. I”, Magyar Tud. Akad. Mat. Kutató Int. Közl., 9 (1964), 495–502 | MR

[5] Freud G., “Über die approximation reeller functionen durch rationale gebrochene functionen”, Acta Mathematica Academiae Scientiarum Hungaricae, 17:3–4 (1966), 313–324 | DOI | MR | Zbl

[6] Gonchar A. A., “O skorosti ratsionalnoi approksimatsii nepreryvnykh funktsii s kharakternymi osobennostyami”, Matem. sb., 73(115) (1967), 630–638 | Zbl

[7] Gonchar A. A., “Otsenki rosta ratsionalnykh funktsii i nekotorye ikh prilozheniya”, Matem. sb., 72(114) (1967), 489–503 | Zbl

[8] Fikhtengolts G. M., Kurs differentsialnogo i integralnogo ischisleniya, t. II, Fizmatgiz, M., 1962

[9] Gradshtein I. S., Ryzhik I. M., Tablitsy integralov, summ, ryadov i proizvedenii, Fizmatgiz, M., 1963 | MR