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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
DOI: https://doi.org/10.1090/S0002-9947-1992-1088019-1
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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Additional Information

DOI: https://doi.org/10.1090/S0002-9947-1992-1088019-1
Keywords: Generalized second-order derivatives, epi-convergence, Mosco convergence, epi-derivatives, proto-derivatives, integral functionals, normal integrands
Article copyright: © Copyright 1992 American Mathematical Society

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