Geodesic
An exact constant on the estimation of the approximation error of classes of differentiable functions by the second-order Cesaro means
Matematičeskie trudy, Tome 24 (2021) no. 2, pp. 150-159.

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

In the article, we study a problem related to the approximation of continuous functions by linear methods. In the class of functions satisfying Lipschitz condition, we obtain the best constant for the approximation by Cesaro means of second order. 
@article{MT_2021_24_2_a8,
     author = {O. G. Rovenskaya},
     title = {An exact constant on the estimation of the approximation error of classes of differentiable functions by the second-order {Cesaro} means},
     journal = {Matemati\v{c}eskie trudy},
     pages = {150--159},
     publisher = {mathdoc},
     volume = {24},
     number = {2},
     year = {2021},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MT_2021_24_2_a8/}
}
TY  - JOUR
AU  - O. G. Rovenskaya
TI  - An exact constant on the estimation of the approximation error of classes of differentiable functions by the second-order Cesaro means
JO  - Matematičeskie trudy
PY  - 2021
SP  - 150
EP  - 159
VL  - 24
IS  - 2
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/MT_2021_24_2_a8/
LA  - ru
ID  - MT_2021_24_2_a8
ER  - 
%0 Journal Article
%A O. G. Rovenskaya
%T An exact constant on the estimation of the approximation error of classes of differentiable functions by the second-order Cesaro means
%J Matematičeskie trudy
%D 2021
%P 150-159
%V 24
%N 2
%I mathdoc
%U http://geodesic.mathdoc.fr/item/MT_2021_24_2_a8/
%G ru
%F MT_2021_24_2_a8
O. G. Rovenskaya. An exact constant on the estimation of the approximation error of classes of differentiable functions by the second-order Cesaro means. Matematičeskie trudy, Tome 24 (2021) no. 2, pp. 150-159. http://geodesic.mathdoc.fr/item/MT_2021_24_2_a8/

[1] Bernshtein S. N., “O nailuchshem' priblizhenii nepreryvnykh' funktsii posredstvom' mnogochlenov' dannoi stepeni. II”, Soobsch. Kharkov. matem. obsch. Vtoraya ser., 13:4–5 (1912), 145–194

[2] Bugaets V. P., Martynyuk V. T., “Tochnye konstanty priblizheniya nepreryvnykh funktsii integralami Dzheksona”, Ukr. matem. zh., 26:4 (1974), 435–443 | Zbl

[3] Bugaets V. P., Martynyuk V. T., “Tochnaya konstanta priblizheniya nepreryvnykh funktsii summatornymi operatorami tipa Dzheksona”, Ukr. matem. zh., 29:6 (1977), 791–796 | Zbl

[4] Gavrilyuk V. T., “Priblizhenie nepreryvnykh periodicheskikh funktsii odnoi i dvukh peremennykh polinomami Rogozinskogo interpolyatsionnogo tipa”, Ukr. matem. zh., 25:5 (1973), 637–648 | Zbl

[5] Gradshtein I. S., Ryzhik I. M., Tablitsy integralov, summ, ryadov i proizvedenii, Fizmatgiz, M., 1971

[6] Dudas V. A., “Priblizhenie nepreryvnykh periodicheskikh funktsii summami Feiera”, Voprosy teorii priblizheniya funktsii i ee prilozhenii, In-t matematiki AN USSR, Kiev, 1976, 106–115

[7] Zastavnyi V. P., “Tochnaya otsenka priblizheniya nekotorykh klassov differentsiruemykh funktsii svertochnymi operatorami”, Ukr. matem. vestn., 7:3 (2010), 409–433

[8] Zigmund A., Trigonometricheskie ryady, v. 1, Mir, M., 1965

[9] Martynyuk V. T., “O priblizhenii differentsiruemykh funktsii srednimi Chezaro”, Ukr. matem. zh., 1990, no. 1, 75–83 | Zbl

[10] Natanson B. P., Konstruktivnaya teoriya funktsii, Gostekhteoretizdat, M., 1949

[11] Nikolskii C. M., “Ob asimptoticheskom povedenii ostatka pri priblizhenii funktsii, udovletvoryayuschikh usloviyu Lipshitsa, summami Feiera”, Izv. AN SSSR. Ser. matem., 4:6 (1940), 501–508

[12] Nikolskii C. M., “Otsenka ostatka summ Feiera dlya periodicheskikh funktsii, imeyuschikh ogranichennuyu proizvodnuyu”, Dokl. AN SSSR, 31:3 (1941), 210–214

[13] Nikolskii C. M., “Priblizhenie periodicheskikh funktsii trigonometricheskimi polinomami”, Tr. MIAN SSSR, 15, 1945, 3–76

[14] Ryzhankova G. I., “O priblizhenii differentsiruemykh funktsii srednimi Chezaro”, Sib. matem. zhurn., 17:1 (1976), 228–232 | Zbl

[15] Stechkin S. B., “O priblizhenii nepreryvnykh periodicheskikh funktsii summami Favara”, Tr. MIAN SSSR, 109, 1971, 26–34 | Zbl

[16] Falaleev L. P., “O tochnykh konstantakh dlya matrichnykh metodov summirovaniya”, Sib. matem. zhurn., 36:4 (1995), 927–933 | Zbl

[17] Nagy Sz. B., “Approximation der Funktionen durch die arithmetischen Mittel ihrer Fourierschen Reihen”, Acta Sci. Math., 11:1–2 (1946), 71–84 | Zbl

[18] Nagy B., “Fuggvenyek megkozelitese Fourier-sorok szamtani kozepeivel”, Math. Fiz. Lapok., 49 (1942), 123–138 | Zbl

[19] Schurer F., Steutel F., “On the degree of approximation by the operators of de la Vallee Poussin”, Monatsh. Math., 87 (1979), 53–64 | DOI | Zbl

[20] Schurer F., Steutel F., “On the degree of approximation of functions in $C^1_{2\pi}$ with operators of the Jackson type”, J. Approx. Theory, 27 (1979), 153–178 | DOI | Zbl

[21] Wang Xing-hua, “The exact constant of approximation of continuois functions by the Jackson singular integral”, Acta Math. Sinica, 14:2 (1964), 231–237 | Zbl