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On a Mean Interpolating the Logarithmic and Identric Means
International Journal of Open Problems in Computer Science and Mathematics, 2013In this paper, we give a positive answer for an open problem posed by Ra ssouli about a new mean dened in terms of ...
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On the ratio of logarithmic means
1995The logarithmic mean of \(x>0\), \(y>0\) is \(L(x,y)= (x-y)/ (\log x- \log y)\) (supposed to equal its limit, \(x\), if \(y=x\)). The following result and several generalizations are offered. For positive \(x\), \(y\), \(u\), \(v\) \[ \max (x/y, y/x)> \max (u/v, v/u) \tag{1} \] implies \[ [L(x, y)/ L(u, v)]^3> xy(x+ y)/ [uv (u+v)]\tag{2} \] but if in ...
Pearce, Charles E. M., Pecaric, Josip
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On the generalized logarithmic mean
1995Various simple results are presented on the intterpolation of the well-known "min HGA max" inequalities by the Toader's exponential mean and by Stolarsky's generalized logarithmic mean. The strong convexity (concavity) of the generalized logarithic mean is investigated for the Karmanov's optimization problem.
Tudor, Mato, Poganj, Tibor
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Logarithmic mean of positive invertible operators
Banach Journal of Mathematical Analysis, 2023Byoung Jin Choi, Sejong Kim
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Inequality of the AGM and the Logarithmic Mean
SIAM Review, 1991B. C. Carlson, Matti Vuorinen
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Two optimal double inequalities between power mean and logarithmic mean
Computers and Mathematics With Applications, 2010Yu-Ming Chu, Wei-Feng Xia
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Logarithmic mean: Chen's approximation or explicit solution?
Computers and Chemical Engineering, 2019John J J Chen
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