Extensions of vector-valued functions with preservation of derivatives

Martin Koc, Jan Kolar

Research output: Contribution to journalArticlepeer-review

2 Citations (Scopus)

Abstract

Let X and Y be Banach or normed linear spaces and F⊂X a closed set. We apply our recent extension theorem for vector-valued Baire one functions to obtain an extension theorem for vector-valued functions f:F→Y with pre-assigned derivatives, with preservation of differentiability (at every point where the pre-assigned derivative is actually a derivative), preservation of continuity, preservation of (point-wise) Lipschitz property and (for finite dimensional domain X) preservation of strict differentiability and global (eventually local) Lipschitz continuity. This work depends on the paper Extensions of vector-valued Baire one functions with preservation of points of continuity (Koc and Kolář (2016) [20]).

Original languageEnglish
Pages (from-to)343-367
Number of pages25
JournalJournal of Mathematical Analysis and Applications
Volume449
Issue number1
Early online date1 Dec 2016
DOIs
Publication statusPublished - 1 May 2017

Keywords

  • Extensions
  • Partitions of unity
  • Strict differentiability
  • Vector-valued differentiable functions

ASJC Scopus subject areas

  • Analysis
  • Applied Mathematics

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