Displaying similar documents to “Convexity and variation diminishing property for Bernstein polynomials in higher dimensions”

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.

The sharpness of convergence results for q -Bernstein polynomials in the case q > 1

Sofiya Ostrovska (2008)

Czechoslovak Mathematical Journal

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Due to the fact that in the case q > 1 the q -Bernstein polynomials are no longer positive linear operators on C [ 0 , 1 ] , the study of their convergence properties turns out to be essentially more difficult than that for q < 1 . In this paper, new saturation theorems related to the convergence of q -Bernstein polynomials in the case q > 1 are proved.