Bernstein算子的强逆不等式

郭顺生;齐秋兰

数学学报 ›› 2003, Vol. 46 ›› Issue (5) : 891-896.

数学学报 ›› 2003, Vol. 46 ›› Issue (5) : 891-896. DOI: 10.12386/A2003sxxb0118
论文

Bernstein算子的强逆不等式

    郭顺生;齐秋兰
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Strong Converse Inequality for Bernstein Operators

    Shun Sheng GUO,Qiu Lan QI
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摘要

本文对Bernstein算子证明了其强逆不等式,这些不等式曾被Ditzian,Ivanov,Totik,李松等人用不同的方法得到过,但其结果是通常的估计(λ=1),古典的结果(λ=0)没有包含,本文引入κ-泛函K_λ~α(f,t~2)(0≤λ≤1,0<α<2),将已有结果推广到0≤λ≤1的情形。

Abstract

For Bernstein operators, we get the strong converse inequalities. Such inequalities have been proved by Ditzian Z., Ivanov K. G., Totik V. and Li Song with different methods. But these results are only normal estimates (with A = 1), the classical one (with A = 0) is not included. In this paper, we introduce the k-functional and extend the preuious results to a larger case 0< λ<1.

关键词

Bernstein算子 / 强逆不等式 / k-泛函

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郭顺生;齐秋兰. Bernstein算子的强逆不等式. 数学学报, 2003, 46(5): 891-896 https://doi.org/10.12386/A2003sxxb0118
Shun Sheng GUO,Qiu Lan QI. Strong Converse Inequality for Bernstein Operators. Acta Mathematica Sinica, Chinese Series, 2003, 46(5): 891-896 https://doi.org/10.12386/A2003sxxb0118

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