Differentiation in abstract spaces
Abstract
A new definition of differentiation for mappings between topological vector spaces is introduced. It does not require the mapping to be defined on a linear manifold, nor does it require it to be continuous. All of the main theorems of differential calculus hold and all other known definitions of differentiation are included. The new definition can be used for singular mappings and those defined on arbitrary sets. Applications are given.
- Publication:
-
Journal of Differential Equations
- Pub Date:
- 1984
- DOI:
- 10.1016/0022-0396(84)90073-1
- Bibcode:
- 1984JDE....55..330S