On an extremal relation of Bernstein operators
نویسندگان
چکیده
منابع مشابه
On an extremal relation of Bernstein operators
In this note we present a new characterization of Bernstein operators by showing that they are the only solution of a certain extremal relation. © 2006 Elsevier Inc. All rights reserved.
متن کاملAn extremal property of Bernstein operators
We establish a strong version of a known extremal property of Bernstein operators, as well as several characterizations of a related specific class of positive polynomial operators. © 2006 Elsevier Inc. All rights reserved. MSC: 41A36; 26D15
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We show that a certain optimality property of the classical Bernstein operator also holds, when suitably reinterpreted, for generalized Bernstein operators on extended Chebyshev systems.
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In this paper we discuss convergence properties and error estimates of rational Bernstein operators introduced by P. Piţul and P. Sablonnière. It is shown that the rational Bernstein operators converge to the identity operator if and only if the maximal difference between two consecutive nodes is converging to zero. Further a Voronovskaja theorem is given based on the explicit computation of hi...
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Replacing the nested sequence of ""nite" dimensional subspaces by the nested sequence of "closed" subspaces in the classical Bernstein lethargy theorem, we obtain a version of this theorem for the space B(X; Y) of all bounded linear maps. Using this result and some properties of diagonal operators, we investigate conditions under which a suitable pair of Banach spaces form an exact Bernstein pa...
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ژورنال
عنوان ژورنال: Journal of Approximation Theory
سال: 2006
ISSN: 0021-9045
DOI: 10.1016/j.jat.2006.03.004