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New inequalities on the homogeneous functions. (English) Zbl 1216.26017
J. Indones. Math. Soc. 15, No. 1, 49-59 (2009); corrigendum ibid. 21, No. 1, 71-72 (2015).
Summary: We define the homogeneous functions \(Gn_{\mu,r}(a,b)\) and \(gn_{\mu,r}(a,b)\). Further we study properties, relations with means, applications to inequalities and partial derivatives. We also give some applications of these means related to Farey fractions and Ky Fan type inequalities.

MSC:
26E60 Means
26D15 Inequalities for sums, series and integrals
11B57 Farey sequences; the sequences \(1^k, 2^k, \dots\)
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