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Relation between Greek means and various means. (English) Zbl 1199.26083

Summary: We obtain some inequalities between Greek means and various means. Further, we deduced the best possible values of various means with \(Gn_{\mu,r}(a,b)\) and \(gn_{\mu,r}(a,b)\). We also study the partial derivatives of important means and the value of \(\alpha\) of second order partial derivatives.

MSC:

26D15 Inequalities for sums, series and integrals
26D10 Inequalities involving derivatives and differential and integral operators
26E60 Means
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