An extremal property for a class of positive linear operators

An 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

About a class of linear positive operators

In this paper we construct a class of linear positive operators (Lm)m≥1 with the help of some nodes. We study the convergence and we demonstrate the Voronovskaja-type theorem for them. By particularization, we obtain some known operators. 2000 Mathematics Subject Classification: 41A10, 41A25, 41A35, 41A36.

On a General Class of Linear and Positive Operators

Suppose that (Lm)m≥1 is a given sequence of linear and positive operators. Starting with the mentioned sequence, the new sequence (Km)m≥1 of linear and positive operators is constructed. For the operators (Km)m≥1 a convergence theorem and a Voronovskaja-type theorem are established. As particular cases of the general construction, we refined the Bernstein’s operators, the Stancu’s operators, th...

Some Extremal Problems for Positive Definite Matrices and Operators

Let C be a real-valued function defined on the set 9& of all positive definite complex hermitian or real symmetric matrices according as F = C (the complex field) or F = R (the real field). Suppose A, B E 9&. We study the optimization problems of (1) finding max C(X) subject to A X, B X positive semidefinite, (2) finding minG(X) subject to X A, X B positive semidefinite. For a general class of ...

An Extremal Property of Fekete Polynomials