Voronovskaja's Theorem and Iterations for Complex Bernstein Polynomials in Compact Disks

被引:32
作者
Gal, Sorin G. [1 ]
机构
[1] Univ Oradea, Dept Math & Comp Sci, Oradea 410087, Romania
关键词
Complex Bernstein polynomials; Voronovskaja's theorem; iterates; univalence; starlikeness; convexity and spirallikeness;
D O I
10.1007/s00009-008-0148-z
中图分类号
O29 [应用数学];
学科分类号
070104 ;
摘要
In this paper, firstly we prove the Voronovskaja's convergence theorem for complex Bernstein polynomials in compact disks in C, centered at origin, with quantitative estimates of this convergence. Secondly, we study the approximation properties of the iterates of complex Bernstein polynomials and we prove that they preserve in the unit disk (beginning with an index) the univalence, starlikeness, convexity and spirallikeness.
引用
收藏
页码:253 / 272
页数:20
相关论文
共 14 条
[1]  
ANDRICA D, 1985, IT SEM FUNCT EQ APPR, V85, P5
[2]  
[Anonymous], 2006, P 2006 INT C NUMERIC
[3]  
GAL SG, SHAPE PRESE IN PRESS
[4]  
GAL SG, APPROXIMATION UNPUB
[5]   CONVERGENCE OF EXTENDED BERNSTEIN POLYNOMIALS IN COMPLEX PLANE [J].
GERGEN, JJ ;
PURCELL, WH ;
DRESSEL, FG .
PACIFIC JOURNAL OF MATHEMATICS, 1963, 13 (04) :1171-&
[6]   The limiting semigroup of the Bernstein iterates: Degree of convergence [J].
Gonska, H ;
Rasa, I .
ACTA MATHEMATICA HUNGARICA, 2006, 111 (1-2) :119-130
[7]  
Gonska H., 2006, J APPL FUNCT ANAL, V1, P403
[8]  
HE F, 1984, REAL ANAL EXCHANGE, V9, P578
[9]  
Karlin S., 1970, Journal of Approximation Theory, V3, P310, DOI 10.1016/0021-9045(70)90055-9
[10]   ITERATES OF BERNSTEIN POLYNOMIALS [J].
KELISKY, RP ;
RIVLIN, TJ .
PACIFIC JOURNAL OF MATHEMATICS, 1967, 21 (03) :511-&