Journal ArticleDOI
The Power and Generalized Logarithmic Means
TLDR
The Power and Generalized Logarithmic Means (PGLM) as discussed by the authors is a generalization of the generalized logarithm of the power-and-generalized linear mean.Abstract:
(1980). The Power and Generalized Logarithmic Means. The American Mathematical Monthly: Vol. 87, No. 7, pp. 545-548.read more
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Inequalities for Means in Two Variables
Horst Alzer,Song-liang Qiu +1 more
TL;DR: In this article, various new inequalities involving the logarithmic mean, the identric mean, and the classical arithmetic and geometric means were presented. But none of these inequalities were studied in this paper.
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Optimal evaluation of a Toader-type mean by power mean
TL;DR: In this article, the authors presented the best possible parameters for the Toader, arithmetic, quadratic, and rth power means of a and b, respectively, such that the double inequality holds for all $a, b>0$cffff with $a
eq b$�, and obtained sharp bounds for the complete elliptic integral.
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On some properties of digamma and polygamma functions
TL;DR: In this article, the authors present new and structural inequalities for digamma, polygamma and inverse polygonal polygammas, and also extend, generalize and refine some known inequalities for these important functions.
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On the identric and logarithmic means
TL;DR: In this article, the identric and logarithmic means of positive real numbers were studied and some improvements of known results and new inequalities containing identric means were obtained for monotonic functions having a concave (or concave) inverse function.
References
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Journal ArticleDOI
A hypergeometric mean value
TL;DR: Generalization of hypergeometric mean value from hypergeometrical function without loss of homogeneity - derivation and properties of hyper geometrical mean value as discussed by the authors...
Journal ArticleDOI
A two-parameter homogeneous mean value
TL;DR: The L(s, t; x) mean is a special case of the integral mean as mentioned in this paper, and it can be regarded as a special kind of integral mean, which can be viewed as a kind of homogeneous integral mean.