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Journal of Convex Analysis 24 (2017), No. 1, 305--308
Copyright 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


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

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