Chain differentials with an application to the mathematical fear operator

✍ Scribed by Pierre Bernhard

• Book ID: 103845678
• Publisher: Elsevier Science
• Year: 2005
• Tongue: English
• Weight: 182 KB
• Volume: 62
• Category: Article
• ISSN: 0362-546X
• DOI: 10.1016/j.na.2005.04.027

✦ Synopsis

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 chaindifferentiable 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.