Mathematica Eterna
Open Access

Abstract

Optimal Inequalities for Seiffert and Kr(a, b) Means

Shaoqin Gao

Given two positive real numbers a and b, let A(a, b), G(a, b) and P(a, b) denote their arithmetic mean, geometric mean and Seiffert mean respectively. Let Kr(a, b) = r q 2 3Ar(a, b) + 1 3Gr(a, b) for r > 0. In this paper, we find the greatest value α and the least value β such that the double inequality Kα(a, b) < P(a, b) < Kβ(a, b) holds for all a, b > 0 with a 6= b.