1. Fréchet differentiability of regular locally Lipschitzian functions
- Author
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F. S. Van Vleck and Maria Gieraltowska-Kedzierska
- Subjects
Mathematics::Functional Analysis ,Pure mathematics ,Applied Mathematics ,Mathematical analysis ,Regular polygon ,Fréchet derivative ,Banach space ,Mathematics::General Topology ,Domain (mathematical analysis) ,Separable space ,Fréchet space ,Almost everywhere ,Differentiable function ,Analysis ,Mathematics - Abstract
This paper considers Frechet differentiability almost everywhere in the sense of category of regular, locally Lipschitzian real-valued functions defined on open subsets of a Banach space. It is first shown that, for separable Banach spaces, Clarke's generalized gradient of such a function is a minimal, convex- and compact-valued, upper semicontinuous multifunction. Using a theorem of Christensen and Kenderov it is then shown that, for separable Asplund spaces, such a function is Frechet differentiable on a dense Gδ subset of its domain. more...
- Published
- 1991
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