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
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author Zeng, Xiaolin
Ding, Changying
author_facet Zeng, Xiaolin
Ding, Changying
author_sort Zeng, Xiaolin
collection PubMed
description 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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spelling pubmed-54271712017-05-26 Some results on random smoothness Zeng, Xiaolin Ding, Changying J Inequal Appl Research 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. Springer International Publishing 2017-05-12 2017 /pmc/articles/PMC5427171/ /pubmed/28553061 http://dx.doi.org/10.1186/s13660-017-1386-z Text en © The Author(s) 2017 Open Access This article is distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made.
spellingShingle Research
Zeng, Xiaolin
Ding, Changying
Some results on random smoothness
title Some results on random smoothness
title_full Some results on random smoothness
title_fullStr Some results on random smoothness
title_full_unstemmed Some results on random smoothness
title_short Some results on random smoothness
title_sort some results on random smoothness
topic Research
url 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
work_keys_str_mv AT zengxiaolin someresultsonrandomsmoothness
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