Results 11 to 20 of about 464 (137)
Sharp Generalized Seiffert Mean Bounds for Toader Mean [PDF]
Abstract and Applied Analysis, 2011 For p∈[0,1], the generalized Seiffert mean of two positive numbers a and b is defined by Sp(a,b)=p(a-b)/arctan[2p(a-b)/(a+b ...
Yu-Ming Chu +3 more
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Sharp Bounds for Toader Mean in terms of Arithmetic and Second Contraharmonic Means [PDF]
Journal of Function Spaces, 2015 We present the best possible parameters λ1,μ1∈R and λ2,μ2∈1/2,1 such that double inequalities λ1C(a,b)+1-λ1A(a,b)
Wei-Mao Qian +3 more
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New Sharp Bounds for the Modified Bessel Function of the First Kind and Toader-Qi Mean [PDF]
Mathematics, 2020 Let I v x be he modified Bessel function of the first kind of order v. We prove the double inequality sinh t t cosh 1 / q q t
Zhen-Hang Yang +2 more
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A Sharp Lower Bound for Toader-Qi Mean with Applications [PDF]
Journal of Function Spaces, 2016 We prove that the inequality TQ(a,b)>Lp(a,b) holds for all a,b>0 with a≠b if and only if p≤3/2, where TQ(a,b)=2/π∫0π/2acos2θbsin2θdθ, Lp(a,b)=[(bp-ap)/(p(b-a))]1/p (p≠0), and L0(a,b)=ab are, respectively, the Toader-Qi and p-order logarithmic means of a
Zhen-Hang Yang, Yu-Ming Chu
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Some sharp bounds for Toader-Qi mean of other bivariate means(Toader-Qi平均与其他二元平均的几个确界)
Zhejiang Daxue xuebao. Lixue ban, 2017 研究了Toader-Qi平均TQ（a，b）关于几何平均G（a，b）、对数平均L（a，b）、算术平均A（a，b）和二次平均Q（a，b）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(a，b)的精确不等式，并获得了特殊情形的结果.
XUHuizuo(徐会作) +1 more
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On the generalized power-type Toader mean
Journal of Mathematical Inequalities, 2022 Summary: This paper deals with the so-called generalized power-type Toader mean which is defined by \[ \boldsymbol{T}_n(a, b) = \left(\frac{2}{\pi}\int_0^{\pi/2}\sqrt{a^n\cos^2\theta+b^2\sin^2\theta}d\theta\right)^{2/n} \] for \(a, b > 0\) with non-zero integer \(n\).
Zhao, Tie-Hong +3 more
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Optimal bounds for Toader mean in terms of arithmetic and contraharmonic means [PDF]
Journal of Mathematical Inequalities, 2013 We find the greatest value α1 and α2, and the least values β1 and β2, such that the double inequalities α1C(a,b)+(1 − α1)A(a,b) 0 with ab. As applications, we get new bounds for the complete elliptic integral of the second kind.
Ying-Qing Song +3 more
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Sharp bounds for Toader mean in terms of contraharmonic mean with applications [PDF]
Journal of Mathematical Inequalities, 2013 We find the greatest value λ and the least value μ in (1/2,1) such that the dou- ble inequality C(λa+(1 − λ)b,λb+(1 − λ)a) 0 with ab, and give new bounds for the perimeter of an ellipse. Here, T(a,b )= 2 π/2 0 a 2cos2 θ +b2sin 2 θdθ ,a ndC(a,b )=( a 2 +b 2 )/(a+b) denote the Toader, and contraharmonic means of two positive numbers a and b ...
Yuming Chu, Miao-Kun Wang, Xiao-Yan Ma
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Sharp inequalities for the Toader mean of order -1 in terms of other bivariate means
Journal of Mathematical Inequalities, 2022 Summary: In the article, we present the best possible parameters \(\alpha_1, \alpha_2, \alpha_3, \alpha_4, \beta_1, \beta_2, \beta_3, \beta_4\in\mathbb{R}\) such that the double inequalities \[ \begin{aligned} \frac{\alpha_1}{H(a, b)}+\frac{1-\alpha_1}{G(a, b)} < \frac{1}{T_{-1}(a, b)} < \frac{\beta_1}{H(a, b)}+\frac{1-\beta_1}{H(a, b)}\\ \frac ...
Qian, Wei-Mao +3 more
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Lévy-Khintchine representation of Toader-Qi mean [PDF]
Mathematical Inequalities & Applications, 2018 Summary: In the paper, by virtue of a Lévy-Khintchine representation and an alternative integral representation for the weighted geometric mean, the authors establish a Lévy-Khintchine representation and an alternative integral representation for the Toader-Qi mean, verify that the Toader-Qi mean is a Bernstein function and that the divided difference ...
Qi, Feng, Guo, Bai-Ni
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