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