Journal of Convex Analysis 16 (2009), No. 2, 423--439
Copyright Heldermann Verlag 2009
On Compositions of D.C.Functions and Mappings
Libor Vesely
Dipartimento di Matematica, Universitŕ degli Studi, Via C. Saldini 50, 20133 Milano, Italy
vesely@mat.unimi.it
Ludek Zajícek
Charles University, Faculty of Mathematics and Physics, Sokolovská 83, 186 75 Praha 8, Czech Republic
zajicek@karlin.mff.cuni.cz
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.
Keywords: d.c.function, composition of d.c.functions, d.c.mapping, delta-convex mapping.
MSC: 46B99; 26B25, 52A41
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