Results 1 to 10 of about 3,756,040 (69)

On some inequalities for the identric, logarithmic and related means [PDF]

Journal of Mathematical Inequalities, 2015
8
Sándor, József, Bhayo, Barkat
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A Sharp Double Inequality between Harmonic and Identric Means [PDF]

Abstract and Applied Analysis, 2011
We find the greatest value p and the least value q in (0,1/2) such that the double inequality H(pa + (1 − p)b, pb + (1 − p)a) < I(a, b) < H(qa + (1 − q)b, qb + (1 − q)a) holds for all a, b > 0 with a ≠ b. Here, H(a, b), and I(a, b) denote the harmonic and identric means of two positive numbers a and b, respectively.
Yu-Ming Chu, Miao-Kun Wang, Zi-Kui Wang
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Two inequalities for means [PDF]

International Journal of Mathematics and Mathematical Sciences, 1995
We prove two new inequalities for the identric mean and a mean related to the arithmetic and geometric mean of two numbers.
J. Sandor
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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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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
doaj   +2 more sources

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
exaly   +2 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 Raïssouli
exaly   +2 more sources

Sharp Bounds for Toader-Qi Mean in Terms of Logarithmic and Identric Means [PDF]

Mathematical Inequalities and Applications, 2016
Yu-Ming Chu, Zhen-Hang Yang
exaly   +2 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
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On approximating the modified Bessel function of the first kind and Toader-Qi mean

Journal of Inequalities and Applications, 2016
In the article, we present several sharp bounds for the modified Bessel function of the first kind I 0 ( t ) = ∑ n = 0 ∞ t 2 n 2 2 n ( n ! ) 2 $I_{0}(t)=\sum_{n=0}^{\infty}\frac{t^{2n}}{2^{2n}(n!)^{2}}$ and the Toader-Qi mean T Q ( a , b ) = 2 π ∫ 0 π ...
Zhen-Hang Yang, Yu-Ming Chu
doaj   +1 more source