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On a Counterexample in Analysis
E. S. Polovinkin Moscow Institute of Physics and Technology (State University)
Abstract:
An example of multivalued convex-valued Lipschitz mapping from $\mathbb R^n$ into $\mathbb R^m$ such that, at any point, the support function of this mapping has no mixed derivatives in the sense of Gâteaux with respect to the initial and conjugate variables is constructed.
Keywords:
multivalued convex-valued Lipschitz mapping, support function, convex analysis, Cantor function.
Received: 10.03.2013
Citation:
E. S. Polovinkin, “On a Counterexample in Analysis”, Mat. Zametki, 95:1 (2014), 123–128; Math. Notes, 95:1 (2014), 111–115
Linking options:
https://www.mathnet.ru/eng/mzm10209https://doi.org/10.4213/mzm10209 https://www.mathnet.ru/eng/mzm/v95/i1/p123
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Abstract page: | 638 | Full-text PDF : | 158 | References: | 96 | First page: | 60 |
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