A study of boundedness in probabilistic normed spaces(II)
It was shown in Lafuerza-Guillén, Rodríguez-Lallena and Sempi (1999)that uniform boundedness in a Serstnev PN space (V,\un,\tau,\tau^*), named boundedness in the present setting, of a subset A in V with respect to the strong topology is equivalent to the fact that the probabilistic radius R_A of A i...
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| Format: | info:eu-repo/semantics/article |
| Sprache: | English |
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Nonlinear Analysis
2014
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| Online Zugang: | http://hdl.handle.net/10835/2765 |
| _version_ | 1789406642508398592 |
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| author | Lafuerza Guillén, Bernardo |
| author_facet | Lafuerza Guillén, Bernardo |
| author_sort | Lafuerza Guillén, Bernardo |
| collection | DSpace |
| description | It was shown in Lafuerza-Guillén, Rodríguez-Lallena and Sempi (1999)that uniform boundedness in a Serstnev PN space (V,\un,\tau,\tau^*), named boundedness in the present setting, of a subset A in V with respect to the strong topology is equivalent to the fact that the probabilistic radius R_A of A is an element of D^+.Here we extend the equivalence just mentioned to a larger class of PN spaces, namely those PN spaces that are topological vector spaces (briefly TV spaces), but are not Serstnev PN spaces. We present a characterization of those PN spaces, whether they are TV spaces or not,in which the equivalence holds. Then, a characterization of the Archimedeanmity of triangle function \tau^* of type \tau_{T,L} is given. This work is a partial solution to a problema of comparing the concepts of distributional boundedness (D-bounded in short) and that of boundedness in the sense of associated strong topology. |
| format | info:eu-repo/semantics/article |
| id | oai:repositorio.ual.es:10835-2765 |
| institution | Universidad de Cuenca |
| language | English |
| publishDate | 2014 |
| publisher | Nonlinear Analysis |
| record_format | dspace |
| spelling | oai:repositorio.ual.es:10835-27652023-04-12T19:39:15Z A study of boundedness in probabilistic normed spaces(II) Lafuerza Guillén, Bernardo Mathematics Probabilistic Normed spaces It was shown in Lafuerza-Guillén, Rodríguez-Lallena and Sempi (1999)that uniform boundedness in a Serstnev PN space (V,\un,\tau,\tau^*), named boundedness in the present setting, of a subset A in V with respect to the strong topology is equivalent to the fact that the probabilistic radius R_A of A is an element of D^+.Here we extend the equivalence just mentioned to a larger class of PN spaces, namely those PN spaces that are topological vector spaces (briefly TV spaces), but are not Serstnev PN spaces. We present a characterization of those PN spaces, whether they are TV spaces or not,in which the equivalence holds. Then, a characterization of the Archimedeanmity of triangle function \tau^* of type \tau_{T,L} is given. This work is a partial solution to a problema of comparing the concepts of distributional boundedness (D-bounded in short) and that of boundedness in the sense of associated strong topology. 2014-06-17T09:45:22Z 2014-06-17T09:45:22Z 2010 info:eu-repo/semantics/article Vol. 73.pp. 1127-1135 0362-546X/$ http://hdl.handle.net/10835/2765 en journal homepage: www.elsevier.com/locate/na; doi: 10.1016/j.na.2009.12.037 info:eu-repo/semantics/openAccess Nonlinear Analysis Accepted 16 December 2009 |
| spellingShingle | Mathematics Probabilistic Normed spaces Lafuerza Guillén, Bernardo A study of boundedness in probabilistic normed spaces(II) |
| title | A study of boundedness in probabilistic normed spaces(II) |
| title_full | A study of boundedness in probabilistic normed spaces(II) |
| title_fullStr | A study of boundedness in probabilistic normed spaces(II) |
| title_full_unstemmed | A study of boundedness in probabilistic normed spaces(II) |
| title_short | A study of boundedness in probabilistic normed spaces(II) |
| title_sort | study of boundedness in probabilistic normed spaces(ii) |
| topic | Mathematics Probabilistic Normed spaces |
| url | http://hdl.handle.net/10835/2765 |
| work_keys_str_mv | AT lafuerzaguillenbernardo astudyofboundednessinprobabilisticnormedspacesii AT lafuerzaguillenbernardo studyofboundednessinprobabilisticnormedspacesii |