Geodesic
A Note on n-Subhomogeneity of Periodic Extension of Convex Functions
Journal of convex analysis, Tome 24 (2017) no. 1, pp. 305-308
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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 $k=1,2,...,n-1 , (n\geq 2)$.
Classification : 39B62, 26A51
Mots-clés : Convexity, subhomogenity, subadditivity 
@article{JCA_2017_24_1_JCA_2017_24_1_a19,
     author = {C. Peppo},
     title = {A {Note} on {n-Subhomogeneity} of {Periodic} {Extension} of {Convex} {Functions}},
     journal = {Journal of convex analysis},
     pages = {305--308},
     year = {2017},
     volume = {24},
     number = {1},
     url = {http://geodesic.mathdoc.fr/item/JCA_2017_24_1_JCA_2017_24_1_a19/}
}
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C. Peppo. A Note on n-Subhomogeneity of Periodic Extension of Convex Functions. Journal of convex analysis, Tome 24 (2017) no. 1, pp. 305-308. http://geodesic.mathdoc.fr/item/JCA_2017_24_1_JCA_2017_24_1_a19/