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Journal of Mathematical Inequalities, ISSN 1846-579X, 2011, Volume 5, Issue 4, pp. 551 - 556
The Specht ratio S(h) is the optimal constant in the reverse of the arithmetic-geometric mean inequality, i.e., if 0 < m <= a, b <= M and h = M/m, then (1 -... 
Operator inequality | Specht ratio | Operator means | Kantorovich constant | Young inequality | Arithmetic-geometric-harmonic mean inequality | MATHEMATICS | MATHEMATICS, APPLIED | operator inequality | operator means | arithmetic-geometric-harmonic mean inequality
Journal Article
Journal of inequalities and applications, ISSN 1029-242X, 2019, Volume 2019, Issue 1, pp. 1 - 12
In this paper, we present some new reverse arithmetic-geometric mean inequalities for operators and matrices due to Lin (Stud. Math. 215:187-194, 2013). Among... 
MATHEMATICS | Arithmetic-geometric-harmonic mean | MATHEMATICS, APPLIED | Sector matrix | Positive linear maps | Inequality | Operators (mathematics) | Inequalities | Arithmetic–geometric–harmonic mean
Journal Article
在數學中經常要比較有興趣的各種量之大小,因此就需要藉助不等式的運算。 證明不等式的技巧多樣化,且方法不一。本篇論文主要介紹數學競賽中常見的基本不等式, 與探討證明不等式時經常使用的解題方法。 In many mathematical problems, we are expected to compare the... 
arrangement | 數學歸納 | 排序 | arithmetics-geometric-harmonic | inequality | 變數代換 | 布奴利 | 不等式 | 詹生 | 算幾 | 柯西 | Cauchy
Dissertation
Taiwanese Journal of Mathematics, ISSN 1027-5487, 12/2011, Volume 15, Issue 6, pp. 2721 - 2731
In this paper, we give the sufficient as well as necessary condition of the Schur-convexity and Schur-harmonic-convexity of the generalized Heronian means with... 
Generalized heronian means | Arithmetic-geometric-harmonic means inequalities | Heronian means | Schur-convexity | Schur-geometric-convexity | Schurharmonic-convexity | MATHEMATICS | Schur-harmonic-convexity | Generalized Heronian means | VALUES
Journal Article
Linear Algebra and Its Applications, ISSN 0024-3795, 10/2017, Volume 531, pp. 268 - 280
As extension of the Lie-Trotter product formula, we define the two-variable and multivariate Lie-Trotter means with several examples including the Sagae-Tanabe... 
Arithmetic-geometric-harmonic mean inequalities | Lie-Trotter formula | Inductive mean | Geometric mean | Spectral geometric mean | MATHEMATICS | MATHEMATICS, APPLIED
Journal Article
Journal of Inequalities in Pure and Applied Mathematics, 2009, Volume 10, Issue 4
Journal Article
by Ren, YH
Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A, Matemáticas, ISSN 1578-7303, 06/2020, Volume 114, Issue 3
In this paper, one of our main targets is to present some improvements of Young-type inequalities due to Alzer et al. (Linear Multilinear Algebra... 
Arithmetic-geometric-harmonic | MATHEMATICS | Kantorovich constant | Young-type inequalities | GEOMETRIC MEAN INEQUALITY | Operators (mathematics) | Norms | Scalars | Inequalities
Journal Article
International Journal of Pure and Applied Mathematics, ISSN 1311-8080, 2013, Volume 89, Issue 5, pp. 719 - 730
Journal Article
有關”不等式的理論”的發展,迄今可以說是一直持續不 斷,在整個 發展過程中未必有多少傑出的佳作,但是在平淡中 卻始終不失其重要性, 許多精彩的不等式陸陸續續地被發現出 來,有些不等式經過多方面的探討 與研究之後,甚至成為極具 傳統性,而多數的不等式則仍然是孤立而沒有 關聯,因此仍有 其在的發展空間。... 
harmonic mean | 幾何平均數 | monotonic function | arithmetic mean | 算術平均數 | 單調函數 | convex function | 調和平均數 | 凸函數 | geometric mean
Dissertation
在參考文獻[5]中,K.B.STOLARSKY.定義下列的函數 [x^α-y^α / α(x- y)]^{1/(α-1)}, if α≠0,1,u(α)={ L(x,y) , if α=0, I(x,y) , if α=1.而且證明函數 u(α) 對 α 而言是嚴格遞增的,但是證明的過... 
harmonic mean | 幾何平均數 | Geometric mean | 算術平均數 | logarithmic mean | Arithmetic mean | 調和平均數 | 對數平均數 | identric 平均數 | identric mean
Dissertation
對於不相等正實數x與y,定義它們的算數平均數A(x,y),identric 平均數I(x,y),對數平均 數L(x,y),幾何平均數G(x,y),以及調和平 均數H(x,y)如下: A=A(x,y)=(x+y)/2, I=I(x,y)=(1/e)(x^x/y^y) ^[1/(x-y)]... 
harmonic mean | 幾何平均數 | arithmetic mean | 算術平均數 | logarithmic mean | 艾坦平均數 | 調和平均數 | 對數平均數 | identric mean | geometric mean
Dissertation
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