Global Bounds for the Generalized Jensen Functional with Applications

Abstract

In this article we give sharp global bounds for the generalized Jensen functional Jn(g,h;p,x). In particular, exact bounds are determined for the generalized power mean in terms from the class of Stolarsky means. As a consequence, we obtain the best possible global converses of quotients and differences of the generalized arithmetic, geometric and harmonic means.

Keywords

• Jensen functional
• A-G-H inequalities
• global bounds
• power means
• convex functions