Convexity and variation diminishing property for Bernstein polynomials in higher dimensions
Marek Beśka (1989)
Banach Center Publications
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Displaying similar documents to “On the Degre of L1-aproximation by Modified Bernstein Polynomials”
Convexity and variation diminishing property for Bernstein polynomials in higher dimensions
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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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Due to the fact that in the case the -Bernstein polynomials are no longer positive linear operators on the study of their convergence properties turns out to be essentially more difficult than that for In this paper, new saturation theorems related to the convergence of -Bernstein polynomials in the case are proved.
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