scholarly journals New sharp bounds for identric mean in terms of logarithmic mean and arithmetic mean

2012 ◽  
pp. 533-543 ◽  
Author(s):  
Zhen-Hang Yang
Keyword(s):  
Arithmetic Mean ◽  
Logarithmic Mean ◽  
Sharp Bounds ◽  
Identric Mean

scholarly journals Sharp Bounds by the Generalized Logarithmic Mean for the Geometric Weighted Mean of the Geometric and Harmonic Means

2012 ◽  
Vol 2012 ◽  
pp. 1-8 ◽  
Author(s):  
Wei-Mao Qian ◽  
Bo-Yong Long
Keyword(s):  
Logarithmic Mean ◽  
Weighted Mean ◽  
Sharp Bounds ◽  
Harmonic Means

We present sharp upper and lower generalized logarithmic mean bounds for the geometric weighted mean of the geometric and harmonic means.

scholarly journals Sharp bounds for Neuman means in terms of two-parameter contraharmonic and arithmetic mean

2019 ◽  
Vol 2019 (1) ◽  
Author(s):  
Wei-Mao Qian ◽  
Zai-Yin He ◽  
Hong-Wei Zhang ◽  
Yu-Ming Chu
Keyword(s):  
Arithmetic Mean ◽  
Sharp Bounds ◽  
Two Parameter

scholarly journals Optimal Inequalities among Various Means of Two Arguments

2009 ◽  
Vol 2009 ◽  
pp. 1-10 ◽  
Author(s):  
Ming-yu Shi ◽  
Yu-ming Chu ◽  
Yue-ping Jiang
Keyword(s):  
Geometric Mean ◽  
Arithmetic Mean ◽  
Power Mean ◽  
Logarithmic Mean ◽  
Optimal Inequalities

We establish two optimal inequalities among power meanMp(a,b)=(ap/2+bp/2)1/p, arithmetic meanA(a,b)=(a+b)/2, logarithmic meanL(a,b)=(a−b)/(log⁡a−log⁡b), and geometric meanG(a,b)=ab.

scholarly journals AN INEQUALITY OF GRUSS' TYPE FOR RIEMANN-STIELTJES INTEGRAL AND APPLICATIONS FOR SPECIAL MEANS

1998 ◽  
Vol 29 (4) ◽  
pp. 287-292
Author(s):  
S. S. DRAGOMIR ◽  
I. FEDOTOV
Keyword(s):  
Stieltjes Integral ◽  
Logarithmic Mean ◽  
Special Means ◽  
Identric Mean

In this paper we derive a new inequality ofGruss' type for Riemann-Stieltjes integral and apply it for special means (logarithmic mean, identric mean, etc·. ·).

scholarly journals Fractional Integral Inequalities for Some Convex Functions

2021 ◽  
Vol 104 (4) ◽  
pp. 14-27
Author(s):  
B.R. Bayraktar ◽  
◽  
A.Kh. Attaev ◽  
Keyword(s):  
Convex Functions ◽  
Fractional Integral ◽  
Arithmetic Mean ◽  
Integral Inequalities ◽  
Power Mean ◽  
Logarithmic Mean ◽  
Real Numbers ◽  
Hadamard Inequality ◽  
Special Means

In this paper, we obtained several new integral inequalities using fractional Riemann-Liouville integrals for convex s-Godunova-Levin functions in the second sense and for quasi-convex functions. The results were gained by applying the double Hermite-Hadamard inequality, the classical Holder inequalities, the power mean, and weighted Holder inequalities. In particular, the application of the results for several special computing facilities is given. Some applications to special means for arbitrary real numbers: arithmetic mean, logarithmic mean, and generalized log-mean, are provided.

scholarly journals Note on weighted Carleman-type inequality

2005 ◽  
Vol 2005 (3) ◽  
pp. 475-481 ◽  
Author(s):  
Chao-Ping Chen ◽  
Wing-Sum Cheung ◽  
Feng Qi
Keyword(s):  
Type Inequality ◽  
Arithmetic Mean ◽  
Logarithmic Mean ◽  
Double Inequality ◽  
Carleman Type

A double inequality involving the constanteis proved by using an inequality between the logarithmic mean and arithmetic mean. As an application, we generalize the weighted Carleman-type inequality.

scholarly journals The Optimal Upper and Lower Power Mean Bounds for a Convex Combination of the Arithmetic and Logarithmic Means

2010 ◽  
Vol 2010 ◽  
pp. 1-9 ◽  
Author(s):  
Wei-Feng Xia ◽  
Yu-Ming Chu ◽  
Gen-Di Wang
Keyword(s):  
Convex Combination ◽  
Arithmetic Mean ◽  
Power Mean ◽  
Logarithmic Mean ◽  
Positive Real ◽  
Lower Power ◽  
Double Inequality ◽  
Logarithmic Means

Forp∈ℝ, the power meanMp(a,b)of orderp, logarithmic meanL(a,b), and arithmetic meanA(a,b)of two positive real valuesaandbare defined byMp(a,b)=((ap+bp)/2)1/p, forp≠0andMp(a,b)=ab, forp=0,L(a,b)=(b-a)/(log⁡b-log⁡a), fora≠bandL(a,b)=a, fora=bandA(a,b)=(a+b)/2, respectively. In this paper, we answer the question: forα∈(0,1), what are the greatest valuepand the least valueq, such that the double inequalityMp(a,b)≤αA(a,b)+(1-α)L(a,b)≤Mq(a,b)holds for alla,b>0?

scholarly journals On HT-convexity and Hadamard-type inequalities

2020 ◽  
Vol 2020 (1) ◽  
Author(s):  
Shu-Ping Bai ◽  
Shu-Hong Wang ◽  
Feng Qi
Keyword(s):  
Convex Function ◽  
Convex Functions ◽  
Arithmetic Mean ◽  
Logarithmic Mean ◽  
New Class

AbstractIn the paper, the authors define a new notion of “HT-convex function”, present some Hadamard-type inequalities for the new class of HT-convex functions and for the product of any two HT-convex functions, and derive some inequalities for the arithmetic mean and the p-logarithmic mean. These results generalize corresponding ones for HA-convex functions and MT-convex functions.

scholarly journals Sharp bounds for the Neuman-Sándor mean in terms of generalized logarithmic mean

2012 ◽  
pp. 567-577 ◽  
Author(s):  
Yong-Min Li ◽  
Boyong Long ◽  
Yuming Chu
Keyword(s):  
Logarithmic Mean ◽  
Sharp Bounds
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