Rearrangements and jensen type inequalities related to convexity, superquadracity, strong convexity and 1-quasiconvexity

Abstract

In this paper we derive and discuss some new theorems related to all rearrangements of a given set in Rn , denoted (x) and use the results to prove some new Jensen type inequalities for convex, superquadratic, strongly convex and 1 -quasiconvex functions.