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.
On extensions of d.c. functions and convex functions / L. Vesely, L. Zajicek. - In: JOURNAL OF CONVEX ANALYSIS. - ISSN 0944-6532. - 17:2(2010), pp. 427-440.
On extensions of d.c. functions and convex functions
L. VeselyPrimo
;
2010
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.
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