Nonsmooth Analysis: Differential Calculus of Nondifferentiable Mappings
Open Access
- 1 July 1981
- journal article
- Published by JSTOR in Transactions of the American Mathematical Society
- Vol. 266 (1) , 1-56
- https://doi.org/10.2307/1998386
Abstract
A new approach to local analysis of nonsmooth mappings from one Banach space into another is suggested. The approach is essentially based on the use of set-valued mappings of a special kind, called fans, for local approximation. Convex sets of linear operators provide an example of fans. Generally, fans can be considered a natural set-valued extension of linear operators. The first part of the paper presents a study of fans; the second is devoted to calculus and includes extensions of the main theorems of classical calculus.Keywords
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