2007/06/05 by L. Vesely, Libor Veselý, Vesely, L. +2
Computer Science · Mathematics · #26B25 #46B99 #52A41 #Advanced Banach Space Theory #Classical Analysis and ODEs (math.CA) #FOS: Mathematics #Functional Analysis (math.FA) #Functional Equations Stability Results #Optimization and Variational Analysis #math.CA #math.FA #msc:26B25 #msc:46B99 #msc:52A41
paper · pdf · doi:10.48550/arxiv.0706.0624
19 pages
arxiv created 2007/06/05 · openalex publication_date 2007/06/05 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.