MULTIVARIATE WEIGHTED BERNSTEIN-TYPE INEQUALITY AND ITS APPLICATIONS

被引：0
|
作者：
Cao Feilong [1 ]
Lin Shaobo [2 ]
机构：
[1] China Jiliang Univ, Dept Informat & Math Sci, Hangzhou 310018, Zhejiang, Peoples R China
[2] Xi An Jiao Tong Univ, Inst Informat & Syst Sci, Xian 710049, Peoples R China
来源：
ACTA MATHEMATICA SCIENTIA | 2012年 / 32卷 / 02期
基金：
中国国家自然科学基金;
关键词：
Bernstein-type inequality; Nikol'skii-type inequality; Ul'yanov-type inequality; approximation; POLYNOMIALS;
D O I：
暂无
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
Bernstein inequality played an important role in approximation theory and Fourier analysis. This article first introduces a general system of functions and the so-called multivariate weighted Bernstein, Nikol'skii, and Ul'yanov-type inequalities. Then, the relations among these three inequalities are discussed. Namely, it is proved that a family of functions equipped with Bernstein-type inequality satisfies Nikol'skii-type and Ul'yanov-type inequality. Finally, as applications, some classical inequalities are deduced from the obtained results.
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页码：471 / 482
页数：12
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