V-Prox-Regular Functions in Smooth Banach Spaces
In this paper, we continue the study of the V-prox-regularity that we have started recently for sets. We define an appropriate concept of the V-prox-regularity for functions in reflexive smooth Banach spaces by adapting the one given in Hilbert spaces. Our main goal is to study the relationship betw...
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| Vydáno v: | Journal of function spaces Ročník 2020; číslo 2020; s. 1 - 8 |
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| Hlavní autoři: | , |
| Médium: | Journal Article |
| Jazyk: | angličtina |
| Vydáno: |
Cairo, Egypt
Hindawi Publishing Corporation
2020
Hindawi John Wiley & Sons, Inc Wiley |
| Témata: | |
| ISSN: | 2314-8896, 2314-8888 |
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| Abstract | In this paper, we continue the study of the V-prox-regularity that we have started recently for sets. We define an appropriate concept of the V-prox-regularity for functions in reflexive smooth Banach spaces by adapting the one given in Hilbert spaces. Our main goal is to study the relationship between the V-prox-regularity of a given l.s.c. f and the V-prox-regularity of its epigraph. |
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| AbstractList | In this paper, we continue the study of the V-prox-regularity that we have started recently for sets. We define an appropriate concept of the V-prox-regularity for functions in reflexive smooth Banach spaces by adapting the one given in Hilbert spaces. Our main goal is to study the relationship between the V-prox-regularity of a given l.s.c. f and the V-prox-regularity of its epigraph. In this paper, we continue the study of the V -prox-regularity that we have started recently for sets. We define an appropriate concept of the V -prox-regularity for functions in reflexive smooth Banach spaces by adapting the one given in Hilbert spaces. Our main goal is to study the relationship between the V -prox-regularity of a given l.s.c. f and the V -prox-regularity of its epigraph. |
| Author | Bounkhel, Messaoud Bachar, Mostafa |
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| Cites_doi | 10.1155/2020/4274160 10.1007/s11228-019-00518-z 10.1090/S0002-9947-96-01543-7 10.1155/2015/478437 10.1016/0362-546X(91)90078-F 10.1090/S0002-9947-96-01544-9 10.3390/math8112066 10.1016/j.jmaa.2004.06.003 10.1023/B:SVAN.0000023403.87092.a2 10.1090/s0002-9947-1995-1290725-3 10.1016/j.jmaa.2019.02.064 |
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| Copyright | Copyright © 2020 Messaoud Bounkhel and Mostafa Bachar. Copyright © 2020 Messaoud Bounkhel and Mostafa Bachar. This is an open access article distributed under the Creative Commons Attribution License (the “License”), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. Notwithstanding the ProQuest Terms and Conditions, you may use this content in accordance with the terms of the License. https://creativecommons.org/licenses/by/4.0 |
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| Snippet | In this paper, we continue the study of the V-prox-regularity that we have started recently for sets. We define an appropriate concept of the V-prox-regularity... In this paper, we continue the study of the V -prox-regularity that we have started recently for sets. We define an appropriate concept of the V... |
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| SubjectTerms | Banach spaces Hilbert space Inequality Regularity |
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| Title | V-Prox-Regular Functions in Smooth Banach Spaces |
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