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On extensions of d.c. functions and convex functions

2008/10/08 by Libor Veselý, Vesely, Libor, Luděk Zaj́ıček +1
Computer Science · Mathematics · #26B25 #46B99 #52A41 #Advanced Banach Space Theory #Approximation Theory and Sequence Spaces #FOS: Mathematics #Functional Analysis (math.FA) #Optimization and Variational Analysis

paper · pdf · doi:10.48550/arxiv.0810.1433

openalex publication_date 2008/10/08 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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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