An Effective Characterization of Schur-Convex Functions with Applications. Corrigendum

Abstract

The aim of this corrigendum is to reveal that in some results of our previous paper "An effective characterization of Schur-convex functions with applications" [J. Conv. Anal 14 (2007) 103-1086], and namely in Lemmas 3.1 and 3.3 and in Theorems 3.4 and 3.6, the word "measurable" should be replaced by "continuous". The reason is that the proof of Lemma 3.1 is not adequate to its statement. What it exactly shows is that a continuous function f is convex if and only if it holds the condition (3). In particular, the correct version of Lemma 3.3 is consistent with Propositions C.1 and C.1.c in the book of A. W. Marshall and I. Olkin ["Inequalities: Theory of Majorization and its Applications, Academic Press, New York (1979), p. 64 and 67]. These amendments do not affect the rest of the paper.