On Cluster Points, Continuity, and Boundedness Associated with the Generalized Statistical Convergence in Probabilistic Normed Spaces
We consider the recently introduced notion of ℐ-statistical convergence (Das, Savas and Ghosal, Appl. Math. Lett., 24(9) (2011), 1509–1514, Savas and Das, Appl. Math. Lett. 24(6) (2011), 826–830) in probabilistic normed spaces and in the following (Şençimen and Pehlivan (2008 vol. 26, 2008 vol. 87...
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| Format: | Article |
| Language: | English |
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2014-01-01
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| Series: | Abstract and Applied Analysis |
| Online Access: | http://dx.doi.org/10.1155/2014/909364 |
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| author | Pratulananda Das Kaustubh Dutta Vatan Karakaya |
| author_facet | Pratulananda Das Kaustubh Dutta Vatan Karakaya |
| author_sort | Pratulananda Das |
| collection | DOAJ |
| description | We consider the recently introduced notion of ℐ-statistical convergence (Das, Savas and Ghosal, Appl. Math. Lett., 24(9) (2011), 1509–1514, Savas and Das, Appl. Math. Lett. 24(6) (2011), 826–830) in probabilistic normed spaces and in the following (Şençimen and Pehlivan (2008 vol. 26, 2008 vol. 87, 2009)) we introduce
the notions like strong ℐ-statistical cluster points and extremal limit points, and strong ℐ-statistical continuity and strong ℐ-statistical D-boundedness in probabilistic normed spaces and study some of their important properties. |
| format | Article |
| id | doaj-art-c9aee27373b94d149c5307ba1a776d52 |
| institution | Kabale University |
| issn | 1085-3375 1687-0409 |
| language | English |
| publishDate | 2014-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Abstract and Applied Analysis |
| spelling | doaj-art-c9aee27373b94d149c5307ba1a776d522025-02-03T06:12:32ZengWileyAbstract and Applied Analysis1085-33751687-04092014-01-01201410.1155/2014/909364909364On Cluster Points, Continuity, and Boundedness Associated with the Generalized Statistical Convergence in Probabilistic Normed SpacesPratulananda Das0Kaustubh Dutta1Vatan Karakaya2Department of Mathematics, Jadavpur University, Jadavpur, Kolkata, West Bengal 700032, IndiaDepartment of Mathematics, Jadavpur University, Jadavpur, Kolkata, West Bengal 700032, IndiaDepartment of Mathematical Engineering, Yıldız Technical University, Esenler, 34210 Istanbul, TurkeyWe consider the recently introduced notion of ℐ-statistical convergence (Das, Savas and Ghosal, Appl. Math. Lett., 24(9) (2011), 1509–1514, Savas and Das, Appl. Math. Lett. 24(6) (2011), 826–830) in probabilistic normed spaces and in the following (Şençimen and Pehlivan (2008 vol. 26, 2008 vol. 87, 2009)) we introduce the notions like strong ℐ-statistical cluster points and extremal limit points, and strong ℐ-statistical continuity and strong ℐ-statistical D-boundedness in probabilistic normed spaces and study some of their important properties.http://dx.doi.org/10.1155/2014/909364 |
| spellingShingle | Pratulananda Das Kaustubh Dutta Vatan Karakaya On Cluster Points, Continuity, and Boundedness Associated with the Generalized Statistical Convergence in Probabilistic Normed Spaces Abstract and Applied Analysis |
| title | On Cluster Points, Continuity, and Boundedness Associated with the Generalized Statistical Convergence in Probabilistic Normed Spaces |
| title_full | On Cluster Points, Continuity, and Boundedness Associated with the Generalized Statistical Convergence in Probabilistic Normed Spaces |
| title_fullStr | On Cluster Points, Continuity, and Boundedness Associated with the Generalized Statistical Convergence in Probabilistic Normed Spaces |
| title_full_unstemmed | On Cluster Points, Continuity, and Boundedness Associated with the Generalized Statistical Convergence in Probabilistic Normed Spaces |
| title_short | On Cluster Points, Continuity, and Boundedness Associated with the Generalized Statistical Convergence in Probabilistic Normed Spaces |
| title_sort | on cluster points continuity and boundedness associated with the generalized statistical convergence in probabilistic normed spaces |
| url | http://dx.doi.org/10.1155/2014/909364 |
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