Refined young inequality with Kantorovich constant

Abstract

The Specht ratio S(h) is the optimal constant in the reverse of the arithmetic-geometric mean inequality i.e., if 0 0, μ ∈ [0,1], whereh = b/a and r = min{μ, 1 - μ}. In this paper, we improve it by virtue of the Kantorovich constant, utilizing the refined scalar Young inequality we establish a weighted arithmetic-geometric-harmonic mean inequality for two positive operators. In the remainder of this work we focus on extending the refined weighted arithmetic-harmonic mean inequality to an operator version for another type of improvement. © ELEMENT, Zagreb.