On the best polynomial approximation of $$$(\psi,\beta)$$$-differentiable functions in $$$L_2$$$ space

S.B. Vakarchuk

doi:10.15421/241701

On the best polynomial approximation of $$$(\psi,\beta)$$$-differentiable functions in $$$L_2$$$ space

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

Abstract

On the classes $$$L^{\psi}_{\beta,2}$$$ exact estimates have been obtained for the values of the best polynomial approximations of $$$(\psi,\beta)$$$-differentiable functions, expressed by the averages modulus of continuity $$$\widehat{\omega}(f^{\psi}_{\beta},t)$$$ with a weight $$$\xi(t)$$$. This modulus was introduced by K.V. Runovski and H.J. Schmeisser.

Keywords

best polynomial approximation; modulus of continuity; $$$(\psi,\beta)$$$-derivative; Fourier series

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References

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