Results 21 to 30 of about 329 (93)
International Journal of Mathematics and Mathematical Sciences, 1995 We prove two new inequalities for the identric mean and a mean related to the arithmetic and geometric mean of two numbers.
J. Sandor
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Journal of Function Spaces, Volume 2016, Issue 1, 2016., 2016 We present the best possible parameters α1,β1,α2,β2∈R and α3, β3 ∈ (1/2,1) such that the double inequalities Qα1(a,b)A1-α1(a,b)
Hua Wang +3 more
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A Sharp Lower Bound for Toader‐Qi Mean with Applications
Journal of Function Spaces, Volume 2016, Issue 1, 2016., 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 and b.
Zhen-Hang Yang, Yu-Ming Chu, Kehe Zhu
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The geometric mean is a Bernstein function [PDF]
, 2013 In the paper, the authors establish, by using Cauchy integral formula in the theory of complex functions, an integral representation for the geometric mean of $n$ positive numbers.
Li, Wen-Hui, Qi, Feng, Zhang, Xiao-Jing
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Best Possible Bounds for Yang Mean Using Generalized Logarithmic Mean
Mathematical Problems in Engineering, Volume 2016, Issue 1, 2016., 2016 We prove that the double inequality Lp(a, b) < U(a, b) < Lq(a, b) holds for all a, b > 0 with a ≠ b if and only if p ≤ p0 and q ≥ 2 and find several sharp inequalities involving the trigonometric, hyperbolic, and inverse trigonometric functions, where p0 = 0.5451⋯ is the unique solution of the equation (p+12) 1/p=2π/ on the interval (0, ∞), U(a,b)=(a-b)
Wei-Mao Qian +2 more
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, 2013 For a class of partially ordered means we introduce a notion of the (nontrivial) cancelling mean. A simple method is given which helps to determine cancelling means for well known classes of Holder and Stolarsky ...
Simic, Slavko
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An optimal double inequality between geometric and identric means
Applied Mathematics Letters, 2012 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Wang, Miao-Kun +2 more
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Sharp Power Mean Bounds for the One‐Parameter Harmonic Mean
Journal of Function Spaces, Volume 2015, Issue 1, 2015., 2015 We present the best possible parameters α = α(r) and β = β(r) such that the double inequality Mα(a, b) < Hr(a, b) < Mβ(a, b) holds for all r ∈ (0, 1/2) and a, b > 0 with a ≠ b, where Mp(a, b) = [(ap + bp)/2] 1/p (p ≠ 0) and M0(a, b)=ab and Hr(a, b) = 2[ra + (1 − r)b][rb + (1 − r)a]/(a + b) are the power and one‐parameter harmonic means of a and b ...
Yu-Ming Chu +3 more
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A simple proof of inequalities related to means [PDF]
, 2009 [[journaltype ...
Gou-Sheng Yang, Shuoh-Jung Liu
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On the identric and logarithmic means
Aequationes Mathematicae, 1990 After a survey of existing results, several new ones are offered for the identric mean \(I(a,b)=e^{-1}(a^{-a}b^ b)^{1/(b-a)}\quad (a\neq b),\quad I(a,a)=a,\) the logarithmic mean \(L(a,b)=(b-a)\ln^{- 1}(b/a)\quad (a\neq b),\quad L(a,a)=a\quad (a>0,\quad b>0)\) and the arithmetic and geometric mean; for instance \[ L(a,b)I(a,b)^{t- 1}
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