Results 1 to 10 of about 76 (46)
Sharp two-parameter bounds for the identric mean. [PDF]
J Inequal Appl, 2018 For t∈[0,1/2] $t\in [0,1/2]$ and s≥1 $s\ge 1$, we consider the two-parameter family of means Qt,s(a,b)=Gs(ta+(1−t)b,(1−t)a+tb)A1−s(a,b), $$ Q_{t,s}(a,b)=G^{s}\bigl(ta+(1-t)b,(1-t)a+tb\bigr)A^{1-s}(a,b), $$ where A and G denote the arithmetic and ...
Kouba O.
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Some Comparison Inequalities for Generalized Muirhead and Identric Means [PDF]
Journal of Inequalities and Applications, 2010 For x,y>0, a,b∈ℝ, with a+b≠0, the generalized Muirhead mean M(a,b;x,y) with parameters a and b and the identric mean I(x,y) are defined by M(a,b;x,y)=((xayb+xbya)/2)1/(a+b) and I(x,y)=(1/e)(yy/xx)1/(y−x), x ...
Yu-Ming Chu, Miao-Kun Wang, Ye-Fang Qiu
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Improvements of Logarithmic and Identric Mean Inequalities for Scalars and Operators
Journal of Applied Mathematics, 2023 In this article, we provide refined inequalities for a convex Riemann’s integrable function using refinements of the classical Hermite-Hadamard inequality.
Aliaa Burqan +2 more
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Bounds of the Neuman-Sándor Mean Using Power and Identric Means [PDF]
Abstract and Applied Analysis, 2013 In this paper we find the best possible lower power mean bounds for the Neuman-Sándor mean and present the sharp bounds for the ratio of the Neuman-Sándor and identric means.
Yu-Ming Chu, Bo-Yong Long
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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(
Yu-ming Chu, Ming-yu Shi, Yue-ping Jiang
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New sharp bounds for logarithmic mean and identric mean [PDF]
Journal of Inequalities and Applications, 2013 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Zhen-Hang Yang, Yang Zhen-Hang
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Best Possible Bounds for Neuman-Sándor Mean by the Identric, Quadratic and Contraharmonic Means [PDF]
Abstract and Applied Analysis, 2013 We prove that the double inequalities Iα1(a,b)Q1-α1(a,b)
Tie-Hong Zhao +3 more
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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}
J Sándor
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Two sharp inequalities for Lehmer mean, identric mean and logarithmic mean [PDF]
Journal of Mathematical Inequalities, 2011 For r ∈ R , the Lehmer mean of two positive numbers a and b is defined by Lr(a,b) = ar+1 +br+1 ar +br . In this paper, we establish two sharp inequalities as follows: I(a,b) > L− 6 (a,b) and L(a,b) > L− 3 (a,b) for all a,b > 0 with a = b . Here I(a,b) = 1 e ( bb aa ) 1 b−a and L(a,b) = b−a logb−loga denote the identric mean and logarithmic mean of two ...
Miao-Kun Wang +2 more
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Optimal inequalities related to the logarithmic, identric, arithmetic and harmonic means
Journal of Numerical Analysis and Approximation Theory, 2010 The logarithmic mean \(L(a,b)\), identric mean \(I(a,b)\), arithmeticmean \(A(a,b)\) and harmonic mean \(H(a,b)\) of two positive real values \(a\) and \(b\) are defined by\begin{align*}\label{main}&L(a,b)=\begin{cases}\tfrac{b-a}{\log b-\log a},& a\neq ...
Wei-feng Xia, Chu Yu-Ming
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