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浙江大学学报(理学版)  2017, Vol. 44 Issue (5): 526-530    DOI: 10.3785/j.issn.1008-9497.2017.05.005
数学与计算机科学     
Toader-Qi平均与其他二元平均的几个确界
徐会作1, 钱伟茂2
1. 温州广播电视大学 经管学院, 浙江 温州 325000;
2. 湖州广播电视大学 远程教育学院, 浙江 湖州 313000
Some sharp bounds for Toader-Qi mean of other bivariate means
XU Huizuo1, QIAN Weimao2
1. School of Economics and Management, Wenzhou Broadcast and TV University, Wenzhou 325000, Zhejiang Province, China;
2. School of Distance Education, Huzhou Broadcast and TV University, Huzhou 313000, Zhejiang Province, China
 全文: PDF(850 KB)   HTML  
摘要: 研究了Toader-Qi平均TQab)关于几何平均Gab)、对数平均Lab)、算术平均Aab)和二次平均Qab)若干特殊组合的序关系.运用实分析方法以及第1类Bessel函数的乘积公式,建立若干重要引理,导出了4个关于Toader-Qi平均TQ(ab)的精确不等式,并获得了特殊情形的结果.
关键词: Toader-Qi平均几何平均对数平均算术平均二次平均    
Abstract: This paper study the order relation of some special combinations of geometric mean G(a,b), logarithmic mean L(a,b), arithmetic mean A(a,b) and quadratic mean Q(a,b) for Toader-Qi mean TQ(a,b). By using the method of real analysis in mathematics and the product formula of the first kind Bessel function, several important lemma are established, and four optimal inequalities for Toader-Qi mean TQ(a,b) are found. The results of particular cases are also presented.
Key words: Toader-Qi mean    geometric mean    logarithmic mean    arithmetic mean    quadratic mean
收稿日期: 2016-11-02 出版日期: 2017-05-01
CLC:  O174.6  
基金资助: 浙江广播电视大学科研课题(XKT-15G17).
作者简介: 徐会作(1978-),http://orcid.org/0000-0002-9989-2672,男,讲师,硕士,主要从事平均值不等式研究,E-mail:21888878@qq.com.
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引用本文:

徐会作, 钱伟茂. Toader-Qi平均与其他二元平均的几个确界[J]. 浙江大学学报(理学版), 2017, 44(5): 526-530.

XU Huizuo, QIAN Weimao. Some sharp bounds for Toader-Qi mean of other bivariate means. Journal of ZheJIang University(Science Edition), 2017, 44(5): 526-530.

链接本文:

https://www.zjujournals.com/sci/CN/10.3785/j.issn.1008-9497.2017.05.005        https://www.zjujournals.com/sci/CN/Y2017/V44/I5/526

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