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arXiv · 1404.6338

One Counterexample of Comonotone Approximation of $2π$-periodic Function on Trigonometric Polynomials

M. G. Pleshakov
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Abstract

Let $2s$ points $y_i=-π\le y_{2s}<\ldots 3$, and $n\in\Bbb N$ there a function $f(x):=f(x;s,Y,n,k)$ exists, such that $f\in\bigtriangleup^{(1)}(Y)\bigcap{\Bbb C}^{(1)}$ and $$ E_n^{(1)}(f;Y)>B_Yn^{\frac k3 -1}\frac 1nω_k\left(f';\frac 1n\right), $$ where $B_Y=$const, depending only on $Y$ and $k$; $ω_k$ is the modulus of smoothness of order $k$, of $f$.

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BibTeXRIS

M. G. Pleshakov. 2014-04-25. One Counterexample of Comonotone Approximation of $2π$-periodic Function on Trigonometric Polynomials. https://arxiv.org/abs/1404.6338

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