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On nonconvex subdifferential calculus in Banach spaces. (English) Zbl 0838.49013
The authors study a notion of normal and subdifferential built by means of Fréchet $$\varepsilon$$-normals and a procedure of sequential upper limit. The construction should be compared with that of A. D. Ioffe [Mathematika 36, No. 1, 1-38 (1989; Zbl 0713.49022)] which was otherwise based on topological upper limits. The subdifferential defined by the authors is, in general, nonconvex and even not closed in the weak* topology. Several calculus rules are shown to hold for such a notion.

##### MSC:
 49J52 Nonsmooth analysis 46G05 Derivatives of functions in infinite-dimensional spaces 58C20 Differentiation theory (Gateaux, Fréchet, etc.) on manifolds
##### Keywords:
generalized differentiation; normal; subdifferential
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