Generalizations of the Jensen–Mercer Inequality via Fink’s Identity

Abstract

We generalize an integral Jensen–Mercer inequality to the class of n-convex functions using Fink’s identity and Green’s functions. We study the monotonicity of some linear functionals constructed from the obtained inequalities using the definition of n-convex functions at a point.

Keywords

• Jensen–Mercer inequality
• Fink’s identity
• n-convex functions