Geodesic
On Compositions of D.C.Functions and Mappings
Journal of convex analysis, Tome 16 (2009) no. 2, pp. 423-439

Voir la notice de l'article provenant de la source Heldermann Verlag

A d.c. (delta-convex) function on a normed linear space is a function representable as a difference of two continuous convex functions. We show that an infinite dimensional analogue of Hartman's theorem on stability of d.c.functions under compositions does not hold in general. However, we prove that it holds in some interesting particular cases. Our main results about compositions are proved in the more general context of d.c.mappings between normed linear spaces.
Classification : 46B99, 26B25, 52A41
Mots-clés : d.c.function, composition of d.c.functions, d.c.mapping, delta-convex mapping 
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     author = {L. Vesely and L. Zaj{\'\i}cek},
     title = {On {Compositions} of {D.C.Functions} and {Mappings}},
     journal = {Journal of convex analysis},
     pages = {423--439},
     publisher = {mathdoc},
     volume = {16},
     number = {2},
     year = {2009},
     url = {http://geodesic.mathdoc.fr/item/JCA_2009_16_2_JCA_2009_16_2_a6/}
}
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L. Vesely; L. Zajícek. On Compositions of D.C.Functions and Mappings. Journal of convex analysis, Tome 16 (2009) no. 2, pp. 423-439. http://geodesic.mathdoc.fr/item/JCA_2009_16_2_JCA_2009_16_2_a6/