Paraconvex analysis on -manifolds
| Autor: | S. Rolewicz |
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| Rok vydání: | 2007 |
| Předmět: | |
| Zdroj: | Optimization. 56:49-60 |
| ISSN: | 1029-4945 0233-1934 |
| DOI: | 10.1080/02331930600819589 |
| Popis: | Let be real Banach spaces. Let f(·) be a real-valued locally uniformly approximate convex function defined on an open subset . Let be an open subset. Let σ (·) be a differentiable mapping of ΩX into ΩY such that the differentials of are locally uniformly continuous function of x. Then f(σ (·)) is also a locally uniformly approximate convex function. Therefore the function f(σ (·)) is Frechet differentiable on a dense G δ-set, provided X is an Asplund space, and Gateaux differentiable on a dense G δ-set, provided X is separable. As a consequence, we obtain that a locally uniformly approximate convex function defined on a -manifold is Frechet differentiable on a dense G δ-set, provided is an Asplund space, and Gateaux differentiable on a dense G δ-set, provided E is separable. †Dedicated to Professor Diethard Pallaschke on the occasion of his 65th birthday. |
| Databáze: | OpenAIRE |
| Externí odkaz: |
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