Geodesic
The Properties of Functions and Approximation by Summation Rational Operators on the Real Axis
Matematičeskie zametki, Tome 76 (2004) no. 1, pp. 111-118.

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

In the space $C(\mathbb R)$, we construct special summation operators of Jackson type with rational kernels and under a suitable choice of poles we obtain order estimates for deviations of these operators from functions belonging to certain classes. 
@article{MZM_2004_76_1_a10,
     author = {V. N. Rusak and I. V. Rybachenko},
     title = {The {Properties} of {Functions} and {Approximation} by {Summation} {Rational} {Operators} on the {Real} {Axis}},
     journal = {Matemati\v{c}eskie zametki},
     pages = {111--118},
     publisher = {mathdoc},
     volume = {76},
     number = {1},
     year = {2004},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_2004_76_1_a10/}
}
TY  - JOUR
AU  - V. N. Rusak
AU  - I. V. Rybachenko
TI  - The Properties of Functions and Approximation by Summation Rational Operators on the Real Axis
JO  - Matematičeskie zametki
PY  - 2004
SP  - 111
EP  - 118
VL  - 76
IS  - 1
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/MZM_2004_76_1_a10/
LA  - ru
ID  - MZM_2004_76_1_a10
ER  - 
%0 Journal Article
%A V. N. Rusak
%A I. V. Rybachenko
%T The Properties of Functions and Approximation by Summation Rational Operators on the Real Axis
%J Matematičeskie zametki
%D 2004
%P 111-118
%V 76
%N 1
%I mathdoc
%U http://geodesic.mathdoc.fr/item/MZM_2004_76_1_a10/
%G ru
%F MZM_2004_76_1_a10
V. N. Rusak; I. V. Rybachenko. The Properties of Functions and Approximation by Summation Rational Operators on the Real Axis. Matematičeskie zametki, Tome 76 (2004) no. 1, pp. 111-118. http://geodesic.mathdoc.fr/item/MZM_2004_76_1_a10/

[1] Rusak V. N., Ratsionalnye funktsii kak apparat priblizheniya, Izd-vo Belorus. un-ta, Minsk, 1979

[2] Pekarskii A. A., “Chebyshevskie ratsionalnye priblizheniya v kruge, na okruzhnosti i na otrezke”, Matem. sb., 133:1 (1987), 86–102 | MR | Zbl

[3] Petrushev P. P., Popov V. A., Rational Approximation of Real Functions, Cambridge Univ. Press, Cambridge, 1987 | Zbl

[4] Lorentz G. G., Golitschek M. V., Makovoz Y. J., Constructive Approximation, New York, 1996

[5] Rovba E. A., “Interpolyatsionnye ratsionalnye operatory tipa Feiera i Valle–Pussena”, Matem. zametki, 53:2 (1993), 114–121 | MR | Zbl

[6] Rovba E. A., “Summatornye ratsionalnye operatory tipa Dzheksona”, Matem. zametki, 61:2 (1997), 270–277 | MR | Zbl

[7] Popov V. A., Petrushev P. P., “Tochnyi poryadok nailuchshego ravnomernogo priblizheniya vypuklykh funktsii ratsionalnymi funktsiyami”, Matem. sb., 103:2 (1977), 285–292 | Zbl

[8] Pekarskii A. A., “Ratsionalnye priblizheniya absolyutno nepreryvnykh funktsii s proizvodnoi iz prostranstva Orlicha”, Matem. sb., 117:1 (1982), 114–130 | MR | Zbl

[9] Bulanov A. P., “O poryadke priblizheniya vypuklykh funktsii ratsionalnymi funktsiyami”, Izv. AN SSSR. Ser. matem., 33:5 (1969), 1132–1148 | MR | Zbl

[10] Rusak V. N., Rybachenko I. V., “Ob odnom metode priblizheniya ratsionalnymi funktsiyami”, Dokl. NAN Belarusi, 4:5 (2002), 14–16 | MR