华东师范大学学报（自然科学版） >

2017 >Issue 4: 41 - 51

DOI: https://doi.org/10.3969/j.issn.1000-5641.2017.04.004

数学

Sándor-Yang平均关于一些二元平均凸组合的确界

  • 徐会作
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  • 温州广播电视大学 经管学院, 浙江 温州 325013
徐会作,男,讲师,研究方向为平均值理论、应用统计.E-mail:21888878@qq.com.

收稿日期: 2016-10-17

  网络出版日期: 2017-07-20

基金资助

浙江广播电视大学科研课题（XKT-15G17）

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Sharp bounds for Sándor-Yang means in terms of some bivariate means

  • XU Hui-zuo
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  • School of Economics and Management, Wenzhou Broadcast and TV University, Wenzhou Zhejiang 325013, China

Received date: 2016-10-17

  Online published: 2017-07-20

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摘要

运用精细化的实分析方法，研究了Sándor-Yang平均SQA（a，b）、SQA（a，b）与算术平均A（a，b）和二次平均Q（a，b）凸组合以及算术平均A（a，b）和反调和平均C（a，b）凸组合的序关系.得到了关于Sándor-Yang平均SQA（a，b）、SQA（a，b）的四个精确双向不等式.

关键词： Schwab-Borchardt 平均; Sá; ndor-Yang 平均; 算术平均; 二次平均; 反调和平均

本文引用格式

徐会作 . Sándor-Yang平均关于一些二元平均凸组合的确界[J]. 华东师范大学学报（自然科学版）, 2017 , (4) : 41 -51 . DOI: 10.3969/j.issn.1000-5641.2017.04.004

Abstract

This paper deals with the inequalities involving Sándor-Yang means derived from the Schwab-Borchardt mean using the method of real analysis. The convex com- binations of the arithmetic mean A(a,b) and quadratic Q(a,b) (or contra-harmonic mean C(a,b)) for the Sándor-Yang means SQA(a,b) and SQA(a,b) are disscused. The main results obtained are the sharp bounds of the two convex combinations, namely, the best possible parameters α1, α2, α3, α4, β1, β2, β3, β4 ∈ (0, 1), such that the double inequalities
α1Q(a,b) + (1-α1)A(a,b) < SQA(a,b) < β1Q(a,b) + (1-β1)A(a,b),
α2Q(a,b) + (1-α2)A(a,b) < SQA(a,b) < β2Q(a,b) + (1-β2)A(a,b),
α3C(a,b) + (1-α3)A(a,b) < SQA(a,b) < β3C(a,b) + (1-β3)A(a,b),
α4C(a,b) + (1-α4)A(a,b) < SQA(a,b) < β4C(a,b) + (1 -β4)A(a,b)
hold for all a, b > 0 and a≠b. Here A(a,b), Q(a,b) and C(a,b) denote respectively the classical arithmetic, quadratic, contra-harmonic means of a and b, SQA(a,b) and SQA(a,b) are two Sándor-Yang means derived from the Schwab-Borchardt mean.

Key words： Schwab-Borchardt mean; Sá; ndor-Yang mean; arithmetic mean; quadratic mean; contra-harmonic mean

参考文献

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