Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)



Generalized second-order derivatives of convex functions in reflexive Banach spaces

Author: Chi Ngoc Do
Journal: Trans. Amer. Math. Soc. 334 (1992), 281-301
MSC: Primary 49J52; Secondary 46G05
MathSciNet review: 1088019
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Abstract: Generalized second-order derivatives introduced by Rockafellar in finite-dimensional spaces are extended to convex functions in reflexive Banach spaces. Parallel results are shown in the infinite-dimensional case. A result that plays an important role in applications is that the generalized second-order differentiability is preserved under the integral sign.

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Keywords: Generalized second-order derivatives, epi-convergence, Mosco convergence, epi-derivatives, proto-derivatives, integral functionals, normal integrands
Article copyright: © Copyright 1992 American Mathematical Society