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The logarithmic mean is a mean. (English) Zbl 0884.26015

Let \(x\) and \(y\) be positive numbers. It is well known that the logarithmic mean \(L(x,y)= (x-y)/(\log x-\log y)\) lies between \(x\) and \(y\). The authors show that this simple fact leads to a variety of interesting inequalities concerning means and operators.

MSC:

26D15 Inequalities for sums, series and integrals
47A63 Linear operator inequalities
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