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Improvement of Jensen-Steffensen's inequality for superquadratic functions

In this paper, improvements for superquadratic functions of Jensen-Steffensen's and related inequalities are discussed. For superquadratic functions which are not convex we get inequalities analog to Jensen-Steffensen's inequality for convex functions. For superquadratic functions which are convex (including many useful functions), we get improvements and extensions of Jensen-Steffensen's inequality and related inequalities.

Jensen-Steffensen inequality; superquadratic function; convex function

Proceedings of the Conference Analysis, Inequalities and Homogenization Theory : in honor of Professor Lars-Erik Persson ; 2009., Luleå, Švedska ; Dag Lukkassen, Lech Maligranda, Annette Meidell, Peter Wall (Ur.).