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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 $$1^k, 2^k, \dots$$