Approximation properties of bivariate complex $q$-Bernstein polynomials in the case $q>1$

Title:

Approximation properties of bivariate complex $q$-Bernstein polynomials in the case $q>1$

Creator:

Mahmudov, Nazim I.

Identifier:

https://cdk.lib.cas.cz/client/handle/uuid:2896a203-62cb-4f67-a0f5-6b12036db8c5
uuid:2896a203-62cb-4f67-a0f5-6b12036db8c5

Subject:

$q$-Bernstein polynomials, modulus of continuity, and Voronovskaja type theorem

Type:

model:article and TEXT

Format:

bez média and svazek

Description:

In the paper, we discuss convergence properties and Voronovskaja type theorem for bivariate $q$-Bernstein polynomials for a function analytic in the polydisc $D_{R_{1}}\times D_{R_{2}}=\{z\in C\colon \vert z\vert <R_{1}\} \times \{ z\in C\colon \vert z\vert <R_{1}\}$ for arbitrary fixed $q>1$. We give quantitative Voronovskaja type estimates for the bivariate $q$-Bernstein polynomials for $q>1$. In the univariate case the similar results were obtained by S. Ostrovska: $q$-Bernstein polynomials and their iterates. J. Approximation Theory 123 (2003), 232–255. and S. G. Gal: Approximation by Complex Bernstein and Convolution Type Operators. Series on Concrete and Applicable Mathematics 8. World Scientific, New York, 2009.

Language:

English

Rights:

http://creativecommons.org/publicdomain/mark/1.0/
policy:public

Coverage:

557-566

Source:

Czechoslovak Mathematical Journal | 2012 Volume:62 | Number:2

Harvested from:

CDK

Metadata only:

false