Jensen-Type Inequalities on Time Scales For $n$-Convex Functions

Abstract

By utilizing some scalar inequalities obtained via Hermite's interpolating polynomial, we will obtain lower and upper bounds for the difference in Jensen's inequality and in the Edmundson-Lah-Ribaric inequality in time scale calculus that hold for the class of $n$-convex functions. Main results are then applied to generalized means, with a particular emphasis to power means, and in that way some new reverse relations for generalized and power means that correspond to $n$-convex functions are obtained.