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A study of boundedness in probabilistic normed spaces
dc.contributor.author | Lafuerza Guillén, Bernardo | |
dc.contributor.author | Sempi, Carlo | |
dc.contributor.author | Zhang, Gaoxun | |
dc.date.accessioned | 2014-06-17T08:33:59Z | |
dc.date.available | 2014-06-17T08:33:59Z | |
dc.date.issued | 2010 | |
dc.identifier.citation | Vol. 73 (2010)pp. 1127-1135 | es_ES |
dc.identifier.issn | 0362-546X/$; doi: 10.1016/j.na.2009.12.037 | |
dc.identifier.uri | http://hdl.handle.net/10835/2751 | |
dc.description.abstract | It was shown in Lafuerza-Guillén, Rodríguez- Lallena and Sempi (1999) that uniform boundedness in a Serstnev PN space (V,\un, \tau,\tau^*), (named boundeness 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 charaterization of the Archimedeanity of triangle functions \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. | es_ES |
dc.language.iso | en | es_ES |
dc.publisher | Nonlinear Analysis | es_ES |
dc.source | Accepted 16 December 2009 | es_ES |
dc.subject | Mathematics | es_ES |
dc.subject | Probabilistic Normed Spaces | es_ES |
dc.title | A study of boundedness in probabilistic normed spaces | es_ES |
dc.type | info:eu-repo/semantics/article | es_ES |
dc.relation.publisherversion | journal homepage: www.elsevier.com/locate/na | es_ES |
dc.rights.accessRights | info:eu-repo/semantics/openAccess | es_ES |