Journal Home Page Cumulative Index List of all Volumes Complete Contentsof this Volume Previous Article Journal of Convex Analysis 24 (2017), No. 1, 305--308Copyright Heldermann Verlag 2017 A Note on n-Subhomogeneity of Periodic Extension of Convex Functions Catherine Peppo CFA - Université P. et M. Curie, 4 place Jussieu, Casier 232, 75252 Paris Cedex 05, France catherine.peppo@courriel.upmc.fr [Abstract-pdf] We prove that the T-periodic extension of a convex function $f_{1}:[0;T[ \rightarrow [0;+\infty[$, is n-subhomogeneous if and only if $$A = \lim_{x\to 0^{+}} f_{1}(x)\leq nf_{1}(k \frac{T}{n}) \quad \text{and} \quad B = \lim_{x\to T^{-}}f_{1}(x)\leq nf_{1}(k \frac{T}{n})$$ for every $k=1,2,...,n-1 , (n\geq 2)$. Keywords: Convexity, subhomogenity, subadditivity. MSC: 39B62, 26A51 [ Fulltext-pdf  (85  KB)] for subscribers only.