Results 11 to 20 of about 4,025,397 (266)
The logarithmic mean is a mean [PDF]
Mathematical Communications, 1997 The fact that the logarithmic mean of two positive numbers is a mean, that is, that it lies between those two numbers, is shown to have a number of consequences.
Mond, B. +2 more
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Complete Monotonicity of Logarithmic Mean [PDF]
, 2007 In the article, the logarithmic mean is proved to be completely monotonic and an open problem about the logarithmically complete monotonicity of the extended mean values is ...
Qi, Feng
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Optimal Lower Power Mean Bound for the Convex Combination of Harmonic and Logarithmic Means [PDF]
Abstract and Applied Analysis, 2011 We find the least value λ∈(0,1) and the greatest value p=p(α) such that αH(a,b)+(1−α)L(a,b)>Mp(a,b) for α∈[λ,1) and all a,b>0 with a≠b, where H(a,b), L(a,b), and Mp(a,b) are the harmonic, logarithmic, and p-th power means of two positive numbers a and b,
Yu-Ming Chu, Shan-Shan Wang, Cheng Zong
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Logarithmic Convexity of the One-Parameter Mean Values [PDF]
, 2004 In this article, the logarithmic convexity of the one-parameter mean values J(r) and the monotonicity of the product J(r)J(−r) with r Є R are presented. Some more general results are established.
Qi, Feng, Cheung, Wing Sum
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Schur-convexity of the Extended Mean Values [PDF]
, 2001 In this article, the Schur-convexity of the extended mean values are proved. Consequently, an inequality between the logarithmic mean values and the identity (exponential) mean values is ...
Qi, Feng
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Notes on the Schur-convexity of the Extended Mean Values [PDF]
, 2002 In this article, the Schur-convexities of the weighted arithmetic mean of function and the extended mean values are proved. Moreover, some inequalities involving the arithmetic mean, the harmonic mean, the logarithmic mean, and comparison between the ...
Qi, Feng +3 more
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The Logarithmic Mean Revisited [PDF]
The American Mathematical Monthly, 2019 We present a simple method for establishing several inequalities relating to logarithmic means.
Jameson, G., Mercer, P.R.
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Journal of Inequalities and Applications, 2017 In the article, we prove that the double inequality α L ( a , b ) + ( 1 − α ) T ( a , b ) < NS ( a , b ) < β L ( a , b ) + ( 1 − β ) T ( a , b ) $$ \alpha L(a,b)+(1-\alpha)T(a,b)< \mathit{NS}(a,b)< \beta L(a,b)+(1-\beta)T(a,b) $$ holds for a , b > 0 $a,b>
Jing-Jing Chen +2 more
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Mathematics, 2022 In this paper, using a criteria for the monotonicity of the quotient of two power series, we present some sharp bounds for a generalized logarithmic operator mean and Heinz operator mean by weighted ones of classical operator ones.
Ling Zhu
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Generalization of Some Integral Inequalities for Arithmetic Harmonically Convex Functions
Cumhuriyet Science Journal, 2022 In this study, by using an integral identity, Hölder integral inequality and modulus properties we obtain some new general inequalities of the Hermite-Hadamard and Bullen type for functions whose derivatives in absolute value at certain power are ...
Huriye Kadakal
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