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Functional Equations Involving the Logarithmic Mean
ZAMM - Journal of Applied Mathematics and Mechanics / Zeitschrift für Angewandte Mathematik und Mechanik, 1996AbstractThe paper deals with some recent results concerning a functional equation involving the logarithmic mean which occurs in a heat conduction problem. By reinterpreting the functional equation in an alternative way, nontrivial solution can be found.
Kahlig, P., Matkowski, J.
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A replacement for the logarithmic mean
Chemical Engineering Science, 1984Abstract A new mean has been developed as an approximation to the logarithmic mean. It may be viewed as a refinement of the arithmetic mean: the latter has been a useful approximation in economic analysis [5,6], whilst the new mean should find use both in flowsheeting programs and in rapid rating calculations a in the example above.
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Power and logarithmic means [PDF]
, 2014 The article consists of two parts. The first part deals with quasi-arithmetic means and convex functions. In the second part, using quasi-arithmetic means, we perform power and logarithmic means of two positive numbers. Such well-known means are arithmetic, geometric, harmonic, logarithmic and identric.
Pavić, Zlatko +2 more
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Harmonic, Logarithmic, and Arithmetic Means and Corollaries
The American Mathematical Monthly, 2020For two positive real numbers a and b, their harmonic, logarithmic, and arithmetic means are respectively defined by H(a,b)=21a+1b=2aba+b,L(a,b)=b−a ln b− ln a , and A(a,b)=a+b2 .Theorem.
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Powerful Meanings for Logarithms
The Mathematics Teacher, 2017Support student reasoning by supplementing a common but problematic meaning for logarithms.
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Mean oscillations of the logarithmic function
Ricerche di Matematica, 2012zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Didenko, Victor D. +2 more
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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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