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On weak Hadamard differentiability of convex functions on Banach spaces. (English) Zbl 0886.46050
Summary: We study two variants of weak Hadamard differentiability of continuous convex functions on a Banach space, uniform weak Hadamard differentiability and weak Hadamard directional differentiability, and determine their special properties on Banach spaces which do not contain a subspace topologically isomorphic to $$\ell_1$$.

MSC:
 46G05 Derivatives of functions in infinite-dimensional spaces 46B20 Geometry and structure of normed linear spaces 46A17 Bornologies and related structures; Mackey convergence, etc. 46A03 General theory of locally convex spaces 58C20 Differentiation theory (Gateaux, Fréchet, etc.) on manifolds 46B25 Classical Banach spaces in the general theory
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