The best polynomial approximation, derivatives of fractional order, and widths of classes of functions in $$$L_2$$$

S.B. Vakarchuk; M.B. Vakarchuk

doi:10.15421/241602

The best polynomial approximation, derivatives of fractional order, and widths of classes of functions in $$$L_2$$$

S.B. Vakarchuk (Alfred Nobel Dnipropetrovsk University), https://orcid.org/0000-0002-2562-8844
M.B. Vakarchuk (Oles Honchar Dnipropetrovsk National University)

Abstract

On the classes of $$$2\pi$$$-periodic functions $$${\mathcal{W}}^{\alpha} (K_{\beta}, \Phi)$$$, where $$$\alpha, \beta \in (0;\infty)$$$, defined by $$$K$$$-functionals $$$K_{\beta}$$$, fractional derivatives of order $$$\alpha$$$, and majorants $$$\Phi$$$, the exact values of different $$$n$$$-widths have been computed in the space $$$L_2$$$.

Keywords

the best polynomial approximation; trigonometric polynom; K-functional; fractional derivative of order $$$\alpha$$$; n-width

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References

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