THE r-MONOTONICITY OF GENERALIZED BERNSTEIN POLYNOMIALS

被引：0
|
作者：
Zhu, Laiyi [1 ]
Huang, Zhiyong [1 ]
机构：
[1] Renmin Univ China, Sch Informat, Beijing 100872, Peoples R China
来源：
PROCEEDINGS OF THE EDINBURGH MATHEMATICAL SOCIETY | 2012年 / 55卷
基金：
中国国家自然科学基金;
关键词：
generalized Bernstein polynomial; r-monotonicity; number of sign changes; CONVEXITY;
D O I：
10.1017/S0013091512000016
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
Let f is an element of C[0, 1] and let the B-n(f, q; x) be generalized Bernstein polynomials based on the q-integers that were introduced by Phillips. We prove that if f is r-monotone, then B-n(f, q; x) is r-monotone, generalizing well-known results when q = 1 and the results when r = 1 and r = 2 by Goodman et al. We also prove a sufficient condition for a continuous function to be r-monotone.
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页码：797 / 807
页数：11
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