On ideal convergence of double sequences in probabilistic normed spaces
The notion of ideal convergence is a generalization of statistical convergence wich has been intensively investigated in last few years. For an admisible ideal f in NxN, the aim of the present paper is to introduce the concepts of f-convergence and f^*-convergence for double sequences on probabilist...
| Main Authors: | , |
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| Format: | info:eu-repo/semantics/article |
| Language: | English |
| Published: |
Acta Mathematica Sinica, English Series
2014
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| Subjects: | |
| Online Access: | http://hdl.handle.net/10835/2754 |
| _version_ | 1789406620821749760 |
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| author | Lafuerza Guillén, Bernardo Kumar, Vijay |
| author_facet | Lafuerza Guillén, Bernardo Kumar, Vijay |
| author_sort | Lafuerza Guillén, Bernardo |
| collection | DSpace |
| description | The notion of ideal convergence is a generalization of statistical convergence wich has been intensively investigated in last few years. For an admisible ideal f in NxN, the aim of the present paper is to introduce the concepts of f-convergence and f^*-convergence for double sequences on probabilistic normed spaces (PN spaces for short). We give some relations related to these notions and find conditions on the ideal f for which both the notions coincide. We also define f-Cauchy and f^*-Cauchy double sequences on PN spaces and show that f-convergent double sequences are f-Cauchy on these spaces. We establish example which shows that our method of convergence for double sequences on PN spaces is more general. |
| format | info:eu-repo/semantics/article |
| id | oai:repositorio.ual.es:10835-2754 |
| institution | Universidad de Cuenca |
| language | English |
| publishDate | 2014 |
| publisher | Acta Mathematica Sinica, English Series |
| record_format | dspace |
| spelling | oai:repositorio.ual.es:10835-27542023-04-12T19:38:56Z On ideal convergence of double sequences in probabilistic normed spaces Lafuerza Guillén, Bernardo Kumar, Vijay Mathematics Probabilistic Normed Spaces The notion of ideal convergence is a generalization of statistical convergence wich has been intensively investigated in last few years. For an admisible ideal f in NxN, the aim of the present paper is to introduce the concepts of f-convergence and f^*-convergence for double sequences on probabilistic normed spaces (PN spaces for short). We give some relations related to these notions and find conditions on the ideal f for which both the notions coincide. We also define f-Cauchy and f^*-Cauchy double sequences on PN spaces and show that f-convergent double sequences are f-Cauchy on these spaces. We establish example which shows that our method of convergence for double sequences on PN spaces is more general. 2014-06-17T08:34:44Z 2014-06-17T08:34:44Z 2011-06-23 info:eu-repo/semantics/article DOI: 10.1007/s10114-012-9321-1 http://hdl.handle.net/10835/2754 en Http://www.ActaMath.com info:eu-repo/semantics/openAccess Acta Mathematica Sinica, English Series Pu blished online: February 21, 2012 |
| spellingShingle | Mathematics Probabilistic Normed Spaces Lafuerza Guillén, Bernardo Kumar, Vijay On ideal convergence of double sequences in probabilistic normed spaces |
| title | On ideal convergence of double sequences in probabilistic normed spaces |
| title_full | On ideal convergence of double sequences in probabilistic normed spaces |
| title_fullStr | On ideal convergence of double sequences in probabilistic normed spaces |
| title_full_unstemmed | On ideal convergence of double sequences in probabilistic normed spaces |
| title_short | On ideal convergence of double sequences in probabilistic normed spaces |
| title_sort | on ideal convergence of double sequences in probabilistic normed spaces |
| topic | Mathematics Probabilistic Normed Spaces |
| url | http://hdl.handle.net/10835/2754 |
| work_keys_str_mv | AT lafuerzaguillenbernardo onidealconvergenceofdoublesequencesinprobabilisticnormedspaces AT kumarvijay onidealconvergenceofdoublesequencesinprobabilisticnormedspaces |