Monotonicity of weighted averages of convex functions

IF 0.9 4区数学 Q2 MATHEMATICS

Mathematical Inequalities & Applications Pub Date : 2020-04-01 DOI:10.7153/MIA-2020-23-33

G. Jameson

引用次数: 3

Abstract

We consider weighted averages of the form Bn(W, f ) = ∑r=0 wn,r f (r/n) , where W is a summability matrix and f is convex. Conditions are given for Bn(W, f ) to increase or decrease with n . It decreases whenever W is a Hausdorff mean. The sequence of Bernstein polynomials for a convex function is a special case. Mathematics subject classification (2010): 26D15, 40G05, 41A10.

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凸函数加权平均的单调性

我们考虑形式为Bn（W，f）=∑r=0 wn，rf（r/n）的加权平均，其中W是可和矩阵，f是凸的。给出了Bn（W，f）随n增加或减少的条件。只要W是Hausdorff均值，它就会减小。凸函数的Bernstein多项式序列是一个特例。数学学科分类（2010）：26D15，40G05，41A10。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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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.