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.

引用

页码：797 / 807

页数：11

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