Generalization of Jensen's and Jensen-Steffensen's inequalities and their converses by Lidstone's polynomial and majorization theorem

• Published in: Journal of numerical analysis and approximation theory Vol. 46; no. 1
• Main Authors: Gorana Aras-Gazic, Josip Pecaric, Ana Vukelic
• Format: Journal Article
• Language: English
• Published: Publishing House of the Romanian Academy 21.09.2017
• Subjects: (2n)-convex function; Green function; Jensen inequality; Jensen-Steffensen inequality; Lidstone polynomial; majorization

In this paper, using majorization theorems and Lidstone's interpolating polynomials we obtain results concerning Jensen's and Jensen-Steffensen's inequalities and their converses in both the integral and the discrete case. We give bounds for identities related to these inequalities by...