Communications in Mathematical Analysis

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.

Article information

Source
Commun. Math. Anal., Volume 21, Number 2 (2018), 46-67.

Dates
First available in Project Euclid: 21 December 2018

Mikic, Rozarija; Pecaric, Josip. Jensen-Type Inequalities on Time Scales For $n$-Convex Functions. Commun. Math. Anal. 21 (2018), no. 2, 46--67. https://projecteuclid.org/euclid.cma/1545361386