Some results on random smoothness

Based on the analysis of stratification structure on random normed modules, we first present the notion of random smoothness in random normed modules. Then, we establish the relations between random smoothness and random strict convexity. Finally, a type of Gâteaux differentiability is defined for r...

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Detalles Bibliográficos
Autores principales: Zeng, Xiaolin, Ding, Changying
Formato: Online Artículo Texto
Lenguaje:English
Publicado: Springer International Publishing 2017
Materias:
Research
Acceso en línea:https://www.ncbi.nlm.nih.gov/pmc/articles/PMC5427171/
https://www.ncbi.nlm.nih.gov/pubmed/28553061
http://dx.doi.org/10.1186/s13660-017-1386-z
Descripción
Sumario:Based on the analysis of stratification structure on random normed modules, we first present the notion of random smoothness in random normed modules. Then, we establish the relations between random smoothness and random strict convexity. Finally, a type of Gâteaux differentiability is defined for random norms, and its relation to random smoothness is given. The results are helpful in the further study of geometry of random normed modules.

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