An extension of Levin-Steckin's theorem to uniformly convex and superquadratic functions

摘要

In this paper, some integral inequalities for uniformly convex functions are studied by using unordered submajorization for cumulative functions. Strongly convex functions and superquadratic functions are considered, too. A Levin-Steckin like theorem is obtained for such functions. As applications, some bounds for the Fejer functional are derived. A result on the Schur-convexity of averages of convex functions is extended to uniformly convex functions. Some specifications for symmetric functions are also given. A corollary for symmetric probability density functions is established. A Levin-Steckin type inequality for generalized psi -uniformly convex functions is provided. Some interpretations for Simpson distributions are presented.