Results 121 to 130 of about 464 (137)

Sharp Inequalities for Toader Mean in Terms of Other Bivariate Means

Hacettepe Journal of Mathematics and Statistics, 2023
In the paper, the author discovers the best constants $\alpha_1$, $\alpha_2$, $\alpha_3$, $\beta_1$, $\beta_2$ and $\beta_3$ for the double inequalities \[ \alpha_1 A\left(\frac{a-b}{a+b}\right)^{2n+2} < T(a,b)-\frac{1}{4}C-\frac{3}{4}A-A\sum_{k=1}^{n-1}\frac{(\frac{1}{2},k)^2}{4((k+1)!)^2}\left(\frac{a-b}{a+b}\right)^{2k+2}<\beta_1 A ...
Wei-Dong Jiang
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Optimal Evaluation of a Toader-Type Mean by Power Mean [PDF]

Journal of Inequalities and Applications, 2015
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Yu-Ming Chu, Tiehong Zhao, Ying-Qing Song   +2 more
exaly   +2 more sources

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Sharp Bounds for the Toader Mean in Terms of Arithmetic and Geometric Means

Revista De La Real Academia De Ciencias Exactas, Fisicas Y Naturales - Serie A: Matematicas, 2021
The authors offer sharp lower and upper bounds for a mean of two arguments considered by \textit{G. Toader} [J. Math. Anal. Appl. 218, No. 2, 358--368 (1998; Zbl 0892.26015)], in terms of the arithmetic and geometric mean. In the proofs, the well-known connection between the Toader mean and the complete elliptic integral of second type is used. A basic
Jing-Feng Tian, Zhen-Hang Yang
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A Double Inequality for Bounding Toader Mean by the Centroidal Mean [PDF]

Proceedings of the Indian Academy of Sciences: Mathematical Sciences, 2014
In the paper, the authors find the best numbers $α$ and $β$ such that $$ \overline{C}\bigl(αa+(1-α)b,αb+(1-α)a\bigr)0$ with $a\ne b$, where $\overline{C}(a,b)={2\bigl(a^2+ab+b^2\bigr)}{3(a+b)}$ and $T(a,b)=\frac{2}π\int_{0}^{π/{2}}\sqrt{a^2{\cos^2θ}+b^2{\sin^2θ}}\,dθ$ denote respectively the centroidal mean and Toader mean of two positive numbers $a ...
Feng Qi
exaly   +3 more sources

Sharp Bounds for Toader-Type Means in Terms of Two-Parameter Means

Acta Mathematica Scientia, 2021
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Yang, Yueying, Qian, Weimao, Zhang, Hongwei, Chu, Yuming   +3 more
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Sharp Generalized Seiffert Mean Bounds for the Toader Mean of Order 4

Revista De La Real Academia De Ciencias Exactas, Fisicas Y Naturales - Serie A: Matematicas, 2021
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Tiehong Zhao, Yanlin Li
exaly   +3 more sources

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)
Feng Qi
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Optimal Lehmer Mean Bounds for the Toader Mean

Results in Mathematics, 2011
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Chu, Yu-Ming, Wang, Miao-Kun
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Bounds for Toader Mean in Terms of Arithmetic and Second Seiffert Means

Communications in Mathematics and Applications, 2019
In the article, we prove that the double inequalities \begin{align*} &\alpha_{1}T(a,b)+(1-\alpha_{1})A(a,b) 0\) with \(a\neq b\) if and only if \(\alpha_{1}\leq 3/4\), \(\beta_{1}\geq1\), \(\alpha_{2}\leq 3/4\) and \(\beta_{2}\geq 1\), where \(A(a,b)\), \(TD(a,b)\) and \(T(a,b)\) are the arithmetic, Toader and second Seiffert means of \(a\) and \(b ...
Yu-Ming Chu, Yue-Ping Jiang
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Optimal Combinations Bounds of Root-Square and Arithmetic Means for Toader Mean

Proceedings of the Indian Academy of Sciences: Mathematical Sciences, 2012
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Miao-Kun Wang, Yu-Ming Chu, Song-Liang Qiu   +2 more
exaly   +3 more sources