Geodesic
On one approximation estimate
Vestnik Samarskogo universiteta. Estestvennonaučnaâ seriâ, no. 5 (2011), pp. 53-59
Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

Linear operators satisfying some conditions are considered. The given operators are a particular kind of class $S_{2m}$ operators (by P. P. Korovkin). The estimate of the value $\left|L_n(f,x)-f(x)\right|$ for the $f \in W^2H^\alpha_M$ is received, $L_n$ belongs to the class $S_6$. For the estimate derivation the interpolation method is used, described in the works by Yu. G. Abakumov and O. N. Shestakova.
Keywords: linear operators, approximation estimate, interpolation method. 
@article{VSGU_2011_5_a5,
     author = {M. B. Medegei},
     title = {On one approximation estimate},
     journal = {Vestnik Samarskogo universiteta. Estestvennonau\v{c}na\^a seri\^a},
     pages = {53--59},
     year = {2011},
     number = {5},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/VSGU_2011_5_a5/}
}
TY  - JOUR
AU  - M. B. Medegei
TI  - On one approximation estimate
JO  - Vestnik Samarskogo universiteta. Estestvennonaučnaâ seriâ
PY  - 2011
SP  - 53
EP  - 59
IS  - 5
UR  - http://geodesic.mathdoc.fr/item/VSGU_2011_5_a5/
LA  - ru
ID  - VSGU_2011_5_a5
ER  - 
%0 Journal Article
%A M. B. Medegei
%T On one approximation estimate
%J Vestnik Samarskogo universiteta. Estestvennonaučnaâ seriâ
%D 2011
%P 53-59
%N 5
%U http://geodesic.mathdoc.fr/item/VSGU_2011_5_a5/
%G ru
%F VSGU_2011_5_a5
M. B. Medegei. On one approximation estimate. Vestnik Samarskogo universiteta. Estestvennonaučnaâ seriâ, no. 5 (2011), pp. 53-59. http://geodesic.mathdoc.fr/item/VSGU_2011_5_a5/

[1] Abakumov Yu. G., Zabelina N. A., Shestakova O. N., “O posledovatelnostyakh lineinykh funktsionalov i nekotorykh operatorakh klassa $S_{2m}$”, Sibirskii matematicheskii zhurnal, 2000, no. 2, 247–252 | MR | Zbl

[2] Shestakova O. N., Approksimativnye svoistva nekotorykh operatorov klassa $S_m$ i ikh dvumernykh analogov, avtoref. dis. $\dots$ kand. fiz.-mat. nauk, Vladivostok, 2004, 18 pp.

[3] Abakumov Yu. G., Posledovatelnosti lineinykh funktsionalov i approksimatsionnye svoistva lineinykh operatorov, ChitGU, Chita, 2004, 179 pp.

[4] Korovkin P. P., “Skhodyaschiesya posledovatelnosti lineinykh operatorov”, Uspekhi matematicheskikh nauk, 17:4(106) (1962), 147–152 | MR | Zbl

[5] Bakhvalov N. S., Chislennye metody, Nauka, M., 1975, 632 pp.