Results 11 to 20 of about 5,576,128 (87)

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, Yu-Ming Chu, Gendi Wang   +2 more
exaly   +3 more sources

New sharp bounds for identric mean in terms of logarithmic mean and arithmetic mean [PDF]

Journal of Mathematical Inequalities, 2012
Let x,y>0 with xy. We give new sharp bounds for identric mean I =e −1 (x x /y y ) 1/(x−y) in terms of logarithmic mean L =( x −y)/(lnx −lny) and arithmetic mean A =( x+y)/2: 1 2 L p0 + 1 2 A p0 1/p0 < I < 1 2 L ˜ p0 + 1 2 A ˜ p0 1/ ˜ p0 ,
Zhen-Hang Yang
exaly   +3 more sources

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
doaj   +5 more sources

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
exaly   +3 more sources

On the identric mean of two accretive matrices

Filomat
Intensive studies aiming to extend some matrix means from positive matrices to accretive matrices and to establish some of their properties have been carried out recently. The contribution of this work falls within this framework. We introduce the identric mean of two accretive matrices and we study its properties.
Mustapha Räıssouli
exaly   +3 more sources

Sharp bounds for Toader-Qi mean in terms of logarithmic and identric means [PDF]

Mathematical Inequalities and Applications, 2016
In the article, we prove that the double inequality λ √ L(a,b)I(a,b) < TQ(a,b) < μ √ L(a,b)I(a,b) holds for all a,b > 0 with a = b if and only if λ e/π and μ 1 , and give an affirmative answer to the conjecture proposed by Yang in [39], where L(a,b) = (b−
Zhen-Hang Yang, Yu-Ming Chu
exaly   +3 more sources

Optimal Lehmer Mean Bounds for the Combinations of Identric and Logarithmic Means [PDF]

Chinese Journal of Mathematics, 2013
For any α∈0,1, we answer the questions: what are the greatest values p and λ and the least values q and μ, such that the inequalities Lpa,b<Iαa,bL1-αa,b<Lqa,b and Lλa,b<αIa,b+1-αLa,b<Lμa,b hold for all a,b>0 with a≠b? Here, Ia,b, La,b, and Lpa,b denote the identric, logarithmic, and pth Lehmer means of two positive numbers a and b ...
Shen, Xu-Hui, Gong, Wei-Ming, Chu, Yu-Ming   +2 more
openaire   +3 more sources

An optimal double inequality between geometric and identric means

Applied Mathematics Letters, 2012
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Miao-Kun Wang, Yu-Ming Chu
exaly   +2 more sources

A New Class of Operator Monotone Functions via Operator Means [PDF]

, 2016
In this paper, we obtain a new class of functions, which is developed via the Hermite--Hadamard inequality for convex functions. The well-known one-one correspondence between the class of operator monotone functions and operator connections declares that
Aujla, J. S., Moslehian, M. S., Pal, R., Singh, M.   +3 more
core   +2 more sources

Generalizations on some Hermite-Hadamard type inequalities for differentiable convex functions with applications to weighted means. [PDF]

ScientificWorldJournal, 2014
Some new Hermite‐Hadamard type inequalities for differentiable convex functions were presented by Xi and Qi. In this paper, we present new generalizations on the Xi‐Qi inequalities.
Sroysang B.
europepmc   +2 more sources