Results 131 to 136 of about 439 (136)

Sharp bounds for the Toader mean of order 3 in terms of arithmetic, quadratic and contraharmonic means

Mathematica Slovaca, 2020
Abstract In the article, we present the best possible parameters α 1, β 1, α 2, β 2 ∈ ℝ and α 3, β 3 ∈ [1/2, 1] such that the double inequalities
Yuming Chu, Tiehong Zhao, Honghu Chu
exaly   +3 more sources

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 ...
Miao-Kun Wang, Yuming Chu
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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 ...
Zai-Yin He, Yue-Ping Jiang, Yu-Ming Chu
openaire   +1 more source

Optimal bounds for a Toader-type mean in terms of one-parameter quadratic and contraharmonic means

Journal of Nonlinear Science and Applications, 2016
Yuming Chu, Honghu Chu, Wei-Mao Qian
exaly   +3 more sources

Optimal inequalities for a Toader-type mean by quadratic and contraharmonic means

Journal of Nonlinear Science and Applications, 2017
Summary: In this paper, we present the best possible parameters \(\alpha_i, \beta_i\) (\(i=1,2,3\)) and \(\alpha_4,\beta_4\in(1/2,1)\) such that the double inequalities \[\alpha_1Q(a,b)+(1-\alpha_1)C(a,b)
Ji, Zhengchao, Ding, Qing, Zhao, Tiehong
exaly   +3 more sources

Sharp bounds for the Toader mean by two classes of exponential-type means with applications

Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A. Matemáticas
Tiehong Zhao, Miaokun Wang
openaire   +1 more source