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.
Banach J. Math. Anal.
4(1):
159-169
(2010).
DOI: 10.15352/bjma/1272374678