Geometric and Analytic Connections of the Jensen and Hermite-Hadamard Inequality

Abstract

The aim of this paper is to present connections between the Jensen and Hermite-Hadamard inequality. The study includes convex functions of one and several variables. The basis of the research are convex combinations with the common center.

The Jensen-Mercer Inequality with Infinite Convex Combinations

“…is the discrete form of Jensen's inequality (see [4]). The proof of the inequality in formula (2.2) can be found in [11,Theorem 3.1].…”