Geodesic
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 
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/
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Voir la notice du chapitre de livre provenant de la source Math-Net.Ru

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.

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