On the Taylor Differentiability in Spaces L<sub>p</sub>, 0 < p ≤ ∞
The function \(f\in L_p[I], \;p>0,\) is called \((k,p)\)-differentiable at a point \(x_0\in I\) if there exists an algebraic polynomial of \(\pi\) of degree no more than \(k\) for which holds \( \Vert f-\pi \Vert_{L_p[J_h]} = o(h^{k+\frac{1}{p}}), \) where \(\;J_h=[x_0-h; x_0+h]\cap I.\) At a...
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| Format: | Article |
| Language: | English |
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Yaroslavl State University
2018-06-01
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| Series: | Modelirovanie i Analiz Informacionnyh Sistem |
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| Online Access: | https://www.mais-journal.ru/jour/article/view/690 |