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On certain identities for means. (English) Zbl 0831.26013
Several inequalities are offered as consequences of the identity $\begin{split} (b^{1/3} \ln b+ a^{1/3} a)/ (b^{1/3}- a^{1/3} \ln a)- (b\ln b- a\ln a)/(b- a)=\\ 3a^{1/3} b^{1/3} (a^{1/3}+ b^{1/3}) \ln(b/a)/(b- a).\end{split}$ .

##### MSC:
 26D15 Inequalities for sums, series and integrals