On the estimate of the uniform deviation from the class of functions with bounded third derivative
Trudy Instituta matematiki i mehaniki, Trudy Instituta Matematiki i Mekhaniki UrO RAN, Tome 14 (2008) no. 3, pp. 145-152
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The problem of the uniform approximation of a continuous function on a closed interval by a class of functions with a uniformly bounded third derivative is considered. It is shown that the value of best approximation of a function by this class cannot be estimated linearly in terms of its third-order modulus of continuity. At the same time, such estimates exist for classes with bounded first or second derivatives.
@article{TIMM_2008_14_3_a12,
author = {A. V. Mironenko},
title = {On the estimate of the uniform deviation from the class of functions with bounded third derivative},
journal = {Trudy Instituta matematiki i mehaniki},
pages = {145--152},
publisher = {mathdoc},
volume = {14},
number = {3},
year = {2008},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/TIMM_2008_14_3_a12/}
}
TY - JOUR AU - A. V. Mironenko TI - On the estimate of the uniform deviation from the class of functions with bounded third derivative JO - Trudy Instituta matematiki i mehaniki PY - 2008 SP - 145 EP - 152 VL - 14 IS - 3 PB - mathdoc UR - http://geodesic.mathdoc.fr/item/TIMM_2008_14_3_a12/ LA - ru ID - TIMM_2008_14_3_a12 ER -
%0 Journal Article %A A. V. Mironenko %T On the estimate of the uniform deviation from the class of functions with bounded third derivative %J Trudy Instituta matematiki i mehaniki %D 2008 %P 145-152 %V 14 %N 3 %I mathdoc %U http://geodesic.mathdoc.fr/item/TIMM_2008_14_3_a12/ %G ru %F TIMM_2008_14_3_a12
A. V. Mironenko. On the estimate of the uniform deviation from the class of functions with bounded third derivative. Trudy Instituta matematiki i mehaniki, Trudy Instituta Matematiki i Mekhaniki UrO RAN, Tome 14 (2008) no. 3, pp. 145-152. http://geodesic.mathdoc.fr/item/TIMM_2008_14_3_a12/