Displaying similar documents to “The best algebraic approximation in Hölder norm.”

Bernstein classes

N. Roytwarf, Yosef Yomdin (1997)

Annales de l'institut Fourier

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One of the classical Bernstein inequalities compares the maxima of a polynomial of a given degree on the interval [-1,1] and on the ellipse in the complex plane with the focuses -1, 1 and the semiaxes R . We prove a similar inequality for a branch of an algebraic function of a given degree on the maximal disk of its regularity, with the explicitly given constant, depending on the degree only. In particular, this improves a recent inequality of Fefferman and Narasimhan and answers one...

The Lower Estimate for Bernstein Operator

Gal, Sorin G., Tachev, Gancho T. (2013)

Mathematica Balkanica New Series

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MSC 2010: 41A10, 41A15, 41A25, 41A36 For functions belonging to the classes C2[0; 1] and C3[0; 1], we establish the lower estimate with an explicit constant in approximation by Bernstein polynomials in terms of the second order Ditzian-Totik modulus of smoothness. Several applications to some concrete examples of functions are presented.