Abstract

We show how our recent results on compositions of d.c. functions (and mappings) imply positive results on extensions of d.c. functions (and mappings). Examples answering two natural relevant questions are presented. Two further theorems, concerning extendability of continuous convex functions from a closed subspace of a normed linear space, complement recent results of J. Borwein, V. Montesinos and J. Vanderwerff.

Author information

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

Libor Vesely

Dip. di Matematica, Università 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

Keywords

  • d.c. function
  • d.c. mapping
  • delta-convex mapping
  • convex function
  • extension
  • Banach space

Mathematics Subject Classification

52A41; 26B25, 46B99

Suggested citation

L. Vesely, L. Zajícek. “On Extensions of D. C. Functions and Convex Functions.” Journal of Convex Analysis 17 (2010), No. 2, 427–440.

Copyright Heldermann Verlag 2010