周期函数共凸逼近中的常数

IF 0.9 4区数学 Q2 MATHEMATICS

Mathematical Inequalities & Applications Pub Date : 2021-01-01 DOI:10.7153/MIA-2021-24-14

G. Dzyubenko

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引用次数: 0

摘要

。设2 π周期函数f∈C，在一个周期内，将其凸性改变有限次，甚至多次。我们感兴趣的是通过与f共凸的三角多项式来估计f的近似程度，也就是说，多项式的凸度正好在f的点处改变。我们列出了这种近似的已建立的jackson型估计，其中所涉及的常数依赖于凸变点的位置，并通过构造一个反例表明这种依赖是必不可少的。

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On constants in coconvex approximation of periodic functions

. Let 2 π -periodic function f ∈ C change its convexity ﬁ nitely even many times, in the period. We are interested in estimating the degree of approximation of f by trigonometric polynomials which are coconvex with it, namely, polynomials that change their convexity exactly at the points where f does. We list established Jackson-type estimates of such approximation where the constants involved depend on the location of the points of change of convexity and show that this dependence is essential by constructing a counterexample.

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来源期刊

Mathematical Inequalities & Applications 数学-数学

CiteScore

2.30

自引率

10.00%

发文量

审稿时长

6-12 weeks

期刊介绍： ''Mathematical Inequalities & Applications'' (''MIA'') brings together original research papers in all areas of mathematics, provided they are concerned with inequalities or their role. From time to time ''MIA'' will publish invited survey articles. Short notes with interesting results or open problems will also be accepted. ''MIA'' is published quarterly, in January, April, July, and October.