Nonsmooth analysis: differential calculus of nondifferentiable mappings

Ioffe, A. D.

doi:10.1090/S0002-9947-1981-0613784-7

Nonsmooth analysis: differential calculus of nondifferentiable mappings
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by A. D. Ioffe

Trans. Amer. Math. Soc. 266 (1981), 1-56

DOI: https://doi.org/10.1090/S0002-9947-1981-0613784-7

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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.

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