第一类修正贝塞尔函数中Toader-Qi均值的新锐界

IF 1.1 3区数学 Q1 MATHEMATICS

Journal of Mathematical Inequalities Pub Date : 2022-01-01 DOI:10.7153/jmi-2022-16-44

Cen Li, Zhi-Ming Liu, Shenzhou Zheng

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引用次数: 1

摘要

设A(A,b)、G(A,b)、L (A,b)和TQ(A,b)分别为A,b和b的算术均值、几何均值、对数均值和Toader-Qi均值。设Iv (x)是第一类v阶的修正贝塞尔函数。我们证明了二重不等式√sinh t t Uq (t) < I0 (t) <√sinh t t Up (t)对t >成立，或者等价地，√L (a,b)Uq (a,b) < TQ(a,b) <√L (a,b)Up (a,b)，当且仅当p 11/15和0 < q 2/π，其中Up (t) = pcosh t−4 (p−2 3)，当a = b时，对a,b >成立。

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On new sharp bounds for the Toader-Qi mean involved in the modified Bessel functions of the first kind

Let A(a,b) , G(a,b) , L (a,b) and TQ(a,b) be the arithmetic, geometric, logarithmic and Toader-Qi means of a,b > 0 with a = b , respectively. Let Iv (x) be the modified Bessel functions of the first kind of order v . We prove the double inequality √ sinh t t Uq (t) < I0 (t) < √ sinh t t Up (t) holds for t > 0 , or equivalently, √ L (a,b)Uq (a,b) < TQ(a,b) < √ L (a,b)Up (a,b), holds for a,b > 0 with a = b , if and only if p 11/15 and 0 < q 2/π , where Up (t) = pcosh t−4 ( p− 2 3 )

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来源期刊

Journal of Mathematical Inequalities MATHEMATICS, APPLIED-MATHEMATICS

CiteScore

2.90

自引率

3.40%

发文量

审稿时长

6-12 weeks

期刊介绍： The ''Journal of Mathematical Inequalities'' (''JMI'') presents carefully selected original research articles from all areas of pure and applied mathematics, provided they are concerned with mathematical inequalities and their numerous applications. ''JMI'' will also periodically publish invited survey articles and short notes with interesting results treating the theory of inequalities, as well as relevant book reviews. Only articles written in the English language and in a lucid, expository style will be considered for publication. ''JMI'' primary audience are pure mathematicians, applied mathemathicians and numerical analysts. ''JMI'' is published quarterly; in March, June, September, and December.