Mercer type variants of the Jensen–Steffensen inequality

Abstract

An integral Jensen–Mercer inequality for weights satisfying conditions for the reversed Jensen–Steffensen inequality is proved here. Several integral inequalities involving more than one monotonic functions with reversed Jensen–Steffensen conditions are proved as well. Furthermore, a couple of general companion inequalities related to the integral Jensen–Mercer inequality with reversed Jensen–Steffensen conditions are presented. Applications for the generalization of weighted Ky Fan’s inequality, classical power mean and classical arithmetic, geometric and harmonic mean inequalities involving bounded variation are also given.