Journal of Convex Analysis 17 (2010), No. 2, 427--440
Copyright Heldermann Verlag 2010
On Extensions of D. C. Functions and Convex Functions
Libor Vesely
Dip. 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
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.
Keywords: d.c. function, d.c. mapping, delta-convex mapping, convex function, extension, Banach space.
MSC: 52A41; 26B25, 46B99
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