Lokesha, V.; Nagaraja, K. M.; Simsek, Y. 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. Cited in 1 ReviewCited in 2 Documents MSC: 26E60 Means 26D15 Inequalities for sums, series and integrals 11B57 Farey sequences; the sequences \(1^k, 2^k, \dots\) Keywords:identric mean; Heron mean; logarithmic mean and monotonicity; Farey fractions PDFBibTeX XMLCite \textit{V. Lokesha} et al., J. Indones. Math. Soc. 15, No. 1, 49--59 (2009; Zbl 1216.26017)