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The Lower Estimate for Bernstein Operator

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

Mathematica Balkanica New Series

MSC 2010: 41A10, 41A15, 41A25, 41A36For 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 Rate of Convergence for Linear Shape-Preserving Algorithms

Dmitry Boytsov, Sergei Sidorov (2015)

Concrete Operators

We prove some results which give explicit methods for determining an upper bound for the rate of approximation by means of operators preserving a cone. Thenwe obtain some quantitative results on the rate of convergence for some sequences of linear shape-preserving operators.

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