Geodesic
The rate of decrease of constants in Jackson type inequalities in dependence of the order of modulus of continuity
Zapiski Nauchnykh Seminarov POMI, Analytical theory of numbers and theory of functions. Part 25, Tome 383 (2010), pp. 33-52 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice du chapitre de livre

Jackson type inequalities for moduli of continuity of arbitrary order are established with the use of linear approximation methods. The constants are smaller than known previously. The results are valid in different spaces of periodic and non periodic functions. Bibl. 19 titles. 
@article{ZNSL_2010_383_a1,
     author = {O. L. Vinogradov and V. V. Zhuk},
     title = {The rate of decrease of constants in {Jackson} type inequalities in dependence of the order of modulus of continuity},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {33--52},
     year = {2010},
     volume = {383},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_2010_383_a1/}
}
TY  - JOUR
AU  - O. L. Vinogradov
AU  - V. V. Zhuk
TI  - The rate of decrease of constants in Jackson type inequalities in dependence of the order of modulus of continuity
JO  - Zapiski Nauchnykh Seminarov POMI
PY  - 2010
SP  - 33
EP  - 52
VL  - 383
UR  - http://geodesic.mathdoc.fr/item/ZNSL_2010_383_a1/
LA  - ru
ID  - ZNSL_2010_383_a1
ER  - 
%0 Journal Article
%A O. L. Vinogradov
%A V. V. Zhuk
%T The rate of decrease of constants in Jackson type inequalities in dependence of the order of modulus of continuity
%J Zapiski Nauchnykh Seminarov POMI
%D 2010
%P 33-52
%V 383
%U http://geodesic.mathdoc.fr/item/ZNSL_2010_383_a1/
%G ru
%F ZNSL_2010_383_a1
O. L. Vinogradov; V. V. Zhuk. The rate of decrease of constants in Jackson type inequalities in dependence of the order of modulus of continuity. Zapiski Nauchnykh Seminarov POMI, Analytical theory of numbers and theory of functions. Part 25, Tome 383 (2010), pp. 33-52. http://geodesic.mathdoc.fr/item/ZNSL_2010_383_a1/

[1] A. F. Timan, Teoriya priblizheniya fukntsii deistvitelnogo peremennogo, M., 1960

[2] S. B. Stechkin, “O poryadke nailuchshikh priblizhenii nepreryvnykh funktsii”, Izv. AN SSSR. Ser. mat., 15:3 (1951), 219–242 | MR | Zbl

[3] N. I. Akhiezer, Lektsii po teorii approksimatsii, M.–L., 1947

[4] V. V. Zhuk, “O nekotorykh tochnykh neravenstvakh mezhdu nailuchshimi priblizheniyami i modulyami nepreryvnosti”, Vestn. Leningr. un-ta. Ser. mat., mekh., astr., 1974, no. 1, 21–26 | MR | Zbl

[5] V. V. Zhuk, Approksimatsiya periodicheskikh funktsii, L., 1982 | MR

[6] V. V. Shalaev, “K voprosu o priblizhenii nepreryvnykh periodicheskikh funktsii trigonometricheskimi polinomami”, Issled. po sovr. probl. summirovaniya i priblizheniya funktsii i ikh pril., 8, Dnepropetrovsk, 1977, 39–43

[7] O. L. Vinogradov, “Tochnoe neravenstvo dlya otkloneniya summ Rogozinskogo i vtorogo modulya nepreryvnosti v prostranstve nepreryvnykh periodicheskikh funktsii”, Zap. nauchn. semin. POMI, 247, 1997, 26–45 | MR | Zbl

[8] V. V. Zhuk, Strukturnye svoistva funktsii i tochnost approksimatsii, L., 1984

[9] Yu. A. Brudnyi, “Ob odnoi teoreme lokalnykh nailuchshikh priblizhenii”, Funkts. analiz i teoriya funktsii, 2, Kazan 1964, 43–49

[10] V. V. Zhuk, “Polunormy i moduli nepreryvnosti vysokikh poryadkov”, Trudy S.-Peterburgsk. mat. ob-va, 2, 1993, 116–177 | MR | Zbl

[11] V. V. Zhuk, V. F. Kuzyutin, Approksimatsiya funktsii i chislennoe integrirovanie, SPb., 1995 | MR

[12] S. Foucart, Y. Kryakin, A. Shadrin, “On the exact constant in the Jackson–Stechkin inequality for the uniform metric”, Constr. Approx., 29 (2009), 157–179 | DOI | MR | Zbl

[13] V. I. Ivanov, “O priblizhenii funktsii v prostranstvakh $L_p$”, Mat. zametki, 56:2 (1994), 15–40 | MR | Zbl

[14] O. L. Vinogradov, V. V. Zhuk, “O konstantakh v obobschennoi teoreme Dzheksona dlya lineinykh metodov priblizheniya”, Teoriya priblizhenii, Tez. dokl. Mezhd. konf. (SPb., 6–8 maya, 2010 g.), SPb., 2010, 10–12

[15] B. M. Levitan, Pochti-periodicheskie funktsii, M., 1953

[16] O. L. Vinogradov, “Tochnye neravenstva tipa Dzheksona dlya priblizhenii klassov svertok tselymi funktsiyami konechnoi stepeni”, Algebra i analiz, 17:4 (2005), 59–114 | MR | Zbl

[17] N. I. Akhiezer, Lektsii po teorii approksimatsii, M., 1965

[18] N. P. Korneichuk, Tochnye konstanty v teorii priblizheniya, M., 1987 | MR

[19] O. L. Vinogradov, V. V. Zhuk, “Otsenki funktsionalov s izvestnoi posledovatelnostyu momentov cherez otkloneniya srednikh tipa Steklova”, Zap. nauchn. semin. POMI, 383, 2010, 5–32