Jensen type inequalities for twice differentiable functions

Abstract

In this paper, we give some Jensen-type inequalities forφ:I→R, I= [α,β]⊂R,whereφis a continuousfunction onI,twice differentiable on ̊I= (α,β) and there existsm= infx∈ ̊Iφ′′(x) orM= supx∈ ̊Iφ′′(x).Furthermore, ifφ′′is bounded on ̊I,then we give an estimate, from below and from above of Jenseninequalities.c©2012 NGA. All rights reserved.