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.

Author information

Contact details are reproduced from the original publication and may be historical.

Libor Veselý

Dipartimento di Matematica, Università degli Studi, Via C. Saldini 50, 20133 Milano, Italy

vesely@mat.unimi.it

Luděk Zajíček

Charles University, Faculty of Mathematics and Physics, Sokolovská 83, 186 75 Praha 8, Czech Republic

zajicek@karlin.mff.cuni.cz

Keywords

  • d.c.function
  • composition of d.c.functions
  • d.c.mapping
  • delta-convex mapping

Mathematics Subject Classification

46B99; 26B25, 52A41

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Suggested citation

L. Veselý, L. Zajíček. “On Compositions of D.C.Functions and Mappings.” Journal of Convex Analysis 16 (2009), No. 2, 423–439. https://doi.org/10.68381/jca16023

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Published by Heldermann Verlag, 2009. Rights now held by Banach Press LLC.