2017
Том 69
№ 7

All Issues

On some extremal problems in the theory of approximation of functions in the spaces $S^p,\quad 1 \leq p < \infty$

Shchitov A. N., Vakarchuk S. B.

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Abstract

We consider and study properties of the smoothness characteristics $\Omega_m(f, t)_{S^p},\quad m \in \mathbb{N},\quad t > 0$, of functions $f(x)$ that belong to the space $S^p,\quad 1 \leq p < \infty$, introduced by Stepanets. Exact inequalities of the Jackson type are obtained, and the exact values of the widths of the classes of functions defined by using $\Omega_m(f, t)_{S^p},\quad m \in \mathbb{N},\quad t > 0$ are calculated.

English version (Springer): Ukrainian Mathematical Journal 58 (2006), no. 3, pp 340-356.

Citation Example: Shchitov A. N., Vakarchuk S. B. On some extremal problems in the theory of approximation of functions in the spaces $S^p,\quad 1 \leq p < \infty$ // Ukr. Mat. Zh. - 2006. - 58, № 3. - pp. 303-316.

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