New Inequalities on the Homogeneous Functions

Abstract

Abstract.In this paper, we define the homogeneous functions Gn µ,r (a, b) and gnµ,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 toFarey fractions and Ky Fan type inequalities.

Sharp two-parameter bounds for the identric mean

“…Many articles studying the properties of means of two variables have been published, and there is a large body of mathematical literature about comparing pairs of means. The interested reader may consult [1–3, 5–7, 9–11] and the references therein.…”