A Note on n-Subhomogeneity of Periodic Extension of Convex Functions

Abstract

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)

.

Contact details are reproduced from the original publication and may be historical.

CFA - Université P. et M. Curie, 4 place Jussieu, Casier 232, 75252 Paris Cedex 05, France

39B62, 26A51

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Published by Heldermann Verlag, 2017. Rights now held by Banach Press.