Bernstein–Doetsch-type criteria for the continuity and Lipschitz continuity of convex set-valued mappings
- Авторлар: Marinov A.V.1
-
Мекемелер:
- Institute of Mathematics and Mechanics, Ural Branch
- Шығарылым: Том 94, № 3 (2016)
- Беттер: 667-669
- Бөлім: Mathematics
- URL: https://journals.rcsi.science/1064-5624/article/view/224553
- DOI: https://doi.org/10.1134/S1064562416060193
- ID: 224553
Дәйексөз келтіру
Аннотация
The Bernstein–Doetsch criterion (for convex and midconvex functionals) has been repeatedly generalized to convex and midconvex set-valued mappings F: X → 2Y; continuity and local Lipschitz continuity were understood in the sense of the Hausdorff distance. However, all such results imposed restrictive additional boundedness-type conditions on the images F(x). In this paper, the Bernstein–Doetsch criterion is generalized to arbitrary convex and midconvex set-valued mappings acting on normed linear spaces X,Y.
Авторлар туралы
A. Marinov
Institute of Mathematics and Mechanics, Ural Branch
Хат алмасуға жауапты Автор.
Email: marinov@imm.uran.ru
Ресей, ul. S. Kovalevskoi 16, Yekaterinburg, 620990
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