Extensions of vector-valued functions with preservation of derivatives
Research output: Contribution to journal › Article
Colleges, School and Institutes
- RSJ a.s.
- University of Warwick, Warwick, United Kingdom.
- Institute of Mathematics, Czech Academy of Sciences
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) ).
|Number of pages||25|
|Journal||Journal of Mathematical Analysis and Applications|
|Early online date||1 Dec 2016|
|Publication status||Published - 1 May 2017|