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.
On compositions of d.c. functions and mappings / L. Vesely, L. Zajicek. - In: JOURNAL OF CONVEX ANALYSIS. - ISSN 0944-6532. - 16:2(2009), pp. 423-439.
On compositions of d.c. functions and mappings
L. VeselyPrimo
;
2009
Abstract
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.
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