VORONOVSKAJA'S THEOREM, SHAPE PRESERVING PROPERTIES AND ITERATIONS FOR COMPLEX q-BERNSTEIN POLYNOMIALS

被引：12

作者：

Gal, Sorin G. ^{[1
]}

机构：

[1] Univ Oradea, Dept Math, Oradea 410087, Romania

来源：

STUDIA SCIENTIARUM MATHEMATICARUM HUNGARICA | 2011年 / 48卷 / 01期

关键词：

Complex q-Bernstein polynomials; Voronovskaja's theorem; approximation in compact disks; iterations; starlikeness; convexity and spiral-likeness; CONVERGENCE; SATURATION;

D O I：

10.1556/SScMath.2010.1156

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

In this paper, first we prove Voronovskaja's convergence theorem for complex q-Bernstein polynomials, 0 < q < 1, attached to analytic functions in compact disks in C centered at origin, with quantitative estimate of this convergence. As an application, we obtain the exact order in approximation of analytic functions by the complex q-Bernstein polynomials on compact disks. Finally, we study the approximation properties of their iterates for any q > 0 and we prove that the complex q(n)-Bernstein polynomials with 0 < q(n) < 1 and q(n) -> 1, preserve in the unit disk (beginning with an index) the starlikeness, convexity and spiral-likeness.

引用

页码：23 / 43

页数：21

共 12 条

[1]

Gal S. G., 2008, Shape-Preserving Approximation by Real and Complex Polynomials

[2] Voronovskaja's Theorem and Iterations for Complex Bernstein Polynomials in Compact Disks [J].