Results 11 to 20 of about 439 (136)
Some Inequalities for Bounding Toader Mean [PDF]
Journal of Function Spaces and Applications, 2013 By finding linear relations among differences between two special means, the authors establish some inequalities for bounding Toader mean in terms of the arithmetic, harmonic, centroidal, and contraharmonic means.
Wen-Hui Li, Miao-Miao Zheng
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On Approximating the Toader Mean by Other Bivariate Means [PDF]
Journal of Function Spaces, 2019 In the article, we provide several sharp bounds for the Toader mean by use of certain combinations of the arithmetic, quadratic, contraharmonic, and Gaussian arithmetic-geometric means.
Jun-Li Wang +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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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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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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The best bounds for Toader mean in terms of the centroidal and arithmetic means [PDF]
Filomat, 2014 In the paper, the authors discover the best constants ?1, ?2, ?1, and ?2 for the double inequalities ?1C(a,b) + (1-?1)A(a,b) < T(a,b) < ?1C(a,b) + (1-?1)A(a,b) and ?2/A(a,b) + 1-?2/C(a,b) < 1/T(a,b) < ?2/A(a,b) + 1-?2-C(a,b) to be valid for all a, b > 0 with a ? b, where C(a,b) = 2(a2+ab+b2)/3(a+b), A(a,b) = a+b/2, and T(a,b)
Hua, Yun, Qi, Feng
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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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Arithmetic Means for a Class of Functions and the Modified Bessel Functions of the First Kind
Mathematics, 2019 In the paper, by virtue of the residue theorem in the theory of complex functions, the authors establish several identities between arithmetic means for a class of functions and the modified Bessel functions of the first kind, present several identities ...
Feng Qi, Shao-Wen Yao, Bai-Ni Guo
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