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 | References | Similar Articles | Additional Information
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