Same Bernstein-type construction and its applications
Balcerzak, Marek (2015-12-08T11:33:48Z)
Acta Universitatis Lodziensis. Folia Mathematica
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Displaying similar documents to “Bernstein classes”
Same Bernstein-type construction and its applications
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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.
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We show that in the class of compact, piecewise curves K in , the semialgebraic curves are exactly those which admit a Bernstein (or a van der Corput-Schaake) type inequality for the derivatives of (the traces of) polynomials on K.
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