On some properties of Jensen-Steffensen's functional

Abstract

Motivated by results of S.S. Dragomir, related to superadditivity and monotonicity of discrete Jensen's functional, in this paper we consider Jensen-Steffensen's functional, i.e. Jensen's functional with the conditions derived from Jensen-Steffensen's inequality. We state and prove results for this functional, similar to those of Dragomir, as well as their integral versions. Finally, some applications concerning means are given.