Results 11 to 20 of about 902,467 (342)
Optimal inequalities between Seiffert's mean and power means [PDF]
Mathematical Inequalities & Applications, 2004 For the Seiffert mean \(P(x,y):=(x-y)/[4\arctan (\sqrt{x/y})-\pi ]\), the author proves that the evaluation \(A_{p}\leq P\leq A_{q}\) holds if and only if ...
Peter Hästö
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Two Sharp Inequalities for Power Mean, Geometric Mean, and Harmonic Mean [PDF]
Journal of Inequalities and Applications, 2009 For p∈R, the power mean of order p of two positive numbers a and b is defined by Mp(a,b)=((ap+bp)/2)1/p,p≠0, and Mp(a,b)=ab, p=0. In this paper, we establish two sharp inequalities as follows: (2/3)G(a,b)+(1/3)H(a,b)⩾M−1/3(a,b) and (1/3)G(a,b)+(2/3)H(a,b)⩾M− ...
Yu‐Ming Chu, Weifeng Xia
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Some matrix inequalities for weighted power mean [PDF]
Annals of Functional Analysis, 2016 In this paper, we prove that, for any positive definite matrices A,B, and real numbers ν,μ,p with −1 ...
Maryam Khosravi
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Power mean inequality of generalized trigonometric functions
, 2012 9
Barkat Ali Bhayo +1 more
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New proofs of weighted power mean inequalities and monotonicity for generalized weighted mean values [PDF]
Mathematical Inequalities & Applications, 2000 New proofs of the weighted power mean inequalities, as well as the monotonicity of the generalized weighted means of two parameters, are offered. The first proof uses the classical Cauchy-Schwarz-Buniakowski inequality, while the second one is based on certain integral representations combined with the mean value theorem of differential calculus.
Feng Qi +3 more
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Optimal inequalities involving power-exponential mean, arithmetic mean and geometric mean [PDF]
Journal of Mathematical Inequalities, 2017 Zhen-Hang Yang, Jing-Feng Tian
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A power mean inequality involving the complete elliptic integrals
Rocky Mountain Journal of Mathematics, 2014 In this paper the authors investigate a power mean inequality for a special function which is defined by the complete elliptic integrals.
Gendi Wang, Xiaohui Zhang, Yu‐Ming Chu
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Two optimal double inequalities between power mean and logarithmic mean
Computers & Mathematics with Applications, 2010 AbstractFor p∈R the power mean Mp(a,b) of order p, the logarithmic mean L(a,b) and the arithmetic mean A(a,b) of two positive real values a and b are defined by Mp(a,b)={(ap+bp2)1p,p≠0,ab,p=0,L(a,b)={b−alogb−loga,a≠b,a,a=b and A(a,b)=a+b2, respectively.In this article, we answer the questions: What are the greatest values p and r, and the least values ...
Yu‐Ming Chu, Weifeng Xia
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Exact inequalities involving power mean, arithmetic mean and identric mean
Journal of Numerical Analysis and Approximation Theory, 2011 For \(p\in \mathbb{R}\), the power mean \(M_{p}(a,b)\) of order \(p\), identric mean \(I(a,b)\) and arithmetic mean \(A(a,b)\) of two positive real numbers \(a\) and \(b\) are defined by \begin{equation*} M_{p}(a,b)= \begin{cases} \displaystyle\left(\tfrac{a^{p}+b^{p}}{2}\right)^{1/p}, & p\neq 0,\\ \sqrt{ab}, & p=0, \end{cases} \quad I(a,b ...
Yu‐Ming Chu +2 more
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Optimal Inequalities for Power Means [PDF]
Journal of Applied Mathematics, 2012 We present the best possible power mean bounds for the product for any p > 0, α ∈ (0,1), and all a, b > 0 with a ≠ b. Here, Mp(a, b) is the pth power mean of two positive numbers a and b.
Li, Yong-Min +3 more
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