Results 1 to 10 of about 329 (93)
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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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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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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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 Some Intermediate Mean Values [PDF]
International Journal of Mathematics and Mathematical Sciences, 2013 We give a necessary and sufficient mean condition for the quotient of two Jensen functionals and define a new class of mean values where are continuously differentiable convex functions satisfying the relation , .
Slavko Simic
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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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ON TWO NEW MEANS OF TWO ARGUMENTS III [PDF]
Проблемы анализа, 2018 In this paper we establish two sided inequalities for the following two new means X=X(a,b)=Ae^(G/P-1), Y=Y(a,b)=Ge^(L/A-1), where A, G, L and P are the arithmetic, geometric, logarithmic, and Seiffert means, respectively.
Sandor J., Bhayo B. A.
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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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On some inequalities for the identric, logarithmic and related means [PDF]
Journal of Mathematical Inequalities, 2015 We offer new proofs, refinements as well as new results related to classical means of two variables, including the identric and logarithmic means.Comment:
Bhayo, Barkat Ali, Sándor, József
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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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