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 language | English |
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Pages (from-to) | 343-367 |
Number of pages | 25 |
Journal | Journal of Mathematical Analysis and Applications |
Volume | 449 |
Issue number | 1 |
Early online date | 1 Dec 2016 |
DOIs | |
Publication status | Published - 1 May 2017 |
Keywords
- Extensions
- Partitions of unity
- Strict differentiability
- Vector-valued differentiable functions
ASJC Scopus subject areas
- Analysis
- Applied Mathematics