Abstract

We prove that the T-periodic extension of a convex function f1:[0;T[→[0;+∞[f_{1}:[0;T[ \rightarrow [0;+\infty[, is n-subhomogeneous if and only if A=lim⁡x→0+f1(x)≤nf1(kTn)andB=lim⁡x→T−f1(x)≤nf1(kTn)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≥2)k=1,2,...,n-1, (n\geq 2).

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Keywords

  • Convexity
  • subhomogenity
  • subadditivity

Mathematics Subject Classification

39B62, 26A51

Suggested citation

C. Peppo. “A Note on n-Subhomogeneity of Periodic Extension of Convex Functions.” Journal of Convex Analysis 24 (2017), No. 1, 305–308. https://doi.org/10.68381/jca24020

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