Sharp inequalities of Jackson-Stechkin type for periodic functions in $L_2$ differentiable in the Weyl sense
Trudy Instituta matematiki i mehaniki, Trudy Instituta Matematiki i Mekhaniki UrO RAN, Tome 25 (2019) no. 4, pp. 255-264
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For periodic functions differentiable in the sense of Weyl and belonging to the space $L_{2}$, sharp inequalities of Jackson–Stechkin type are obtained for a special $m$th-order modulus of continuity generated by the Steklov operator (function). Similar characteristics of smoothness of functions were considered earlier by V. A. Abilov, F. V. Abilova, V. M. Kokilashvili, S. B. Vakarchuk, V. I. Zabutnaya, K. Tukhliev, etc. For classes of functions defined in terms of these characteristics, we solve a number of extremal problems of polynomial approximation theory.
Keywords:
best approximation, periodic function, special modulus of continuity, Jackson–Stechkin inequalities, extremal problems.
@article{TIMM_2019_25_4_a26,
author = {M. Sh. Shabozov and A. A. Shabozova},
title = {Sharp inequalities of {Jackson-Stechkin} type for periodic functions in $L_2$ differentiable in the {Weyl} sense},
journal = {Trudy Instituta matematiki i mehaniki},
pages = {255--264},
publisher = {mathdoc},
volume = {25},
number = {4},
year = {2019},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/TIMM_2019_25_4_a26/}
}
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%0 Journal Article %A M. Sh. Shabozov %A A. A. Shabozova %T Sharp inequalities of Jackson-Stechkin type for periodic functions in $L_2$ differentiable in the Weyl sense %J Trudy Instituta matematiki i mehaniki %D 2019 %P 255-264 %V 25 %N 4 %I mathdoc %U http://geodesic.mathdoc.fr/item/TIMM_2019_25_4_a26/ %G ru %F TIMM_2019_25_4_a26
M. Sh. Shabozov; A. A. Shabozova. Sharp inequalities of Jackson-Stechkin type for periodic functions in $L_2$ differentiable in the Weyl sense. Trudy Instituta matematiki i mehaniki, Trudy Instituta Matematiki i Mekhaniki UrO RAN, Tome 25 (2019) no. 4, pp. 255-264. http://geodesic.mathdoc.fr/item/TIMM_2019_25_4_a26/