Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
10426902 | Nonlinear Analysis: Theory, Methods & Applications | 2005 | 9 Pages |
Abstract
We introduce a concept of derivative in a topological vector space that yields the chain rule of differentiation for composition of functions, akin to, but simpler than, the epiderivative of Aubin-Frankowska. We show that if a function has a Gâteaux differential with suitable continuity properties, it is a chain differential. As an example, we show that the mathematical fear operator is chain-differentiable with respect to the cost density distribution in the space of continuous functions endowed with the topology of pointwise convergence uniform on every compact subsets.
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Authors
Pierre Bernhard,