Sub- and superadditive integral means ✩

The integral means are special Cauchy means (see, e.g., [L. Losonczi, On the comparison of Cauchy mean values, J. Inequal. Appl. 7 (2002) 11–24]) depending on one function. The two variable integral means were (independently) defined and studied by Elezovi´c and Pe˘cari´c [Differential and integral f -means and applications to digamma function, Math. Inequal. Appl. 3 (2000) 189–196]. The comparison problem of two integral means (under differentiability conditions) was solved by Losonczi [Comparison and subhomogeneity of integral means, Math. Inequal. Appl. 5 (2000) 609– 618]. Here we completely characterize the additive, sub- and superadditive integral means of n 2 variables.  2005 Elsevier Inc. All rights reserved