Statistical Convergence of Double Sequences on Probabilistic Normed Spaces
The concept of statistical convergence was presented by Steinhaus in 1951. This concept was extended to the double sequences by Mursaleen and Edely in 2003. Karakus has recently introduced the concept of statistical convergence of ordinary (single) sequence on probabilistic normed spaces. In this pa...
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| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
Wiley
2007-01-01
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| Series: | International Journal of Mathematics and Mathematical Sciences |
| Online Access: | http://dx.doi.org/10.1155/2007/14737 |
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| _version_ | 1832549972004831232 |
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| author | S. Karakus K. Demırcı |
| author_facet | S. Karakus K. Demırcı |
| author_sort | S. Karakus |
| collection | DOAJ |
| description | The concept of statistical convergence was presented by Steinhaus in 1951.
This concept was extended to the double sequences by Mursaleen and Edely in
2003. Karakus has recently introduced the concept of statistical convergence
of ordinary (single) sequence on probabilistic normed spaces. In this paper,
we define statistical analogues of convergence and Cauchy for double sequences
on probabilistic normed spaces. Then we display an exampl e such that our
method of convergence is stronger than usual convergence on probabilistic
normed spaces. Also we give a useful characterization for statistically
convergent double sequences. |
| format | Article |
| id | doaj-art-fc159ff1ed63438c9fec691f92f72366 |
| institution | Kabale University |
| issn | 0161-1712 1687-0425 |
| language | English |
| publishDate | 2007-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | International Journal of Mathematics and Mathematical Sciences |
| spelling | doaj-art-fc159ff1ed63438c9fec691f92f723662025-02-03T06:08:12ZengWileyInternational Journal of Mathematics and Mathematical Sciences0161-17121687-04252007-01-01200710.1155/2007/1473714737Statistical Convergence of Double Sequences on Probabilistic Normed SpacesS. Karakus0K. Demırcı1Department of Mathematics, Faculty of Arts and Sciences, Sinop University, Sinop 57000, TurkeyDepartment of Mathematics, Faculty of Arts and Sciences, Sinop University, Sinop 57000, TurkeyThe concept of statistical convergence was presented by Steinhaus in 1951. This concept was extended to the double sequences by Mursaleen and Edely in 2003. Karakus has recently introduced the concept of statistical convergence of ordinary (single) sequence on probabilistic normed spaces. In this paper, we define statistical analogues of convergence and Cauchy for double sequences on probabilistic normed spaces. Then we display an exampl e such that our method of convergence is stronger than usual convergence on probabilistic normed spaces. Also we give a useful characterization for statistically convergent double sequences.http://dx.doi.org/10.1155/2007/14737 |
| spellingShingle | S. Karakus K. Demırcı Statistical Convergence of Double Sequences on Probabilistic Normed Spaces International Journal of Mathematics and Mathematical Sciences |
| title | Statistical Convergence of Double Sequences on Probabilistic Normed Spaces |
| title_full | Statistical Convergence of Double Sequences on Probabilistic Normed Spaces |
| title_fullStr | Statistical Convergence of Double Sequences on Probabilistic Normed Spaces |
| title_full_unstemmed | Statistical Convergence of Double Sequences on Probabilistic Normed Spaces |
| title_short | Statistical Convergence of Double Sequences on Probabilistic Normed Spaces |
| title_sort | statistical convergence of double sequences on probabilistic normed spaces |
| url | http://dx.doi.org/10.1155/2007/14737 |
| work_keys_str_mv | AT skarakus statisticalconvergenceofdoublesequencesonprobabilisticnormedspaces AT kdemırcı statisticalconvergenceofdoublesequencesonprobabilisticnormedspaces |