Displaying similar documents to “Approximation properties of bivariate complex q -Bernstein polynomials in the case q > 1 ”

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.

ω –weighted holomorphic Besov spaces on the unit ball in C n

A. V. Harutyunyan, Wolfgang Lusky (2011)

Commentationes Mathematicae Universitatis Carolinae

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The ω -weighted Besov spaces of holomorphic functions on the unit ball B n in C n are introduced as follows. Given a function ω of regular variation and 0 < p < ∞ , a function f holomorphic in B n is said to belong to the Besov space B p ( ω ) if ∥ f ∥ B p ( ω ) p = ∫ B n ( 1 - | z | 2 ) p | D f ( z ) | p ω ( 1 - | z | ) ( 1 - | z | 2 ) n + 1 d ν ( z ) < + ∞ , where d ν ( z ) is the volume measure on B n and D stands for the fractional derivative of f . The holomorphic Besov space is described in the terms of the corresponding L p ( ω ) space. Some projection theorems and theorems on existence of the inversions of these projections are proved....

Bernstein-type operators on the half line

Antonio Attalienti, Michele Campiti (2002)

Czechoslovak Mathematical Journal

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We define Bernstein-type operators on the half line [ 0 , + ∞ [ by means of two sequences of strictly positive real numbers. After studying their approximation properties, we also establish a Voronovskaja-type result with respect to a suitable weighted norm.