Density by Moduli and Statistical Boundedness
We have generalized the notion of statistical boundedness by introducing the concept of f-statistical boundedness for scalar sequences where f is an unbounded modulus. It is shown that bounded sequences are precisely those sequences which are f-statistically bounded for every unbounded modulus f. A...
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| Format: | Article |
| Language: | English |
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Wiley
2016-01-01
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| Series: | Abstract and Applied Analysis |
| Online Access: | http://dx.doi.org/10.1155/2016/2143018 |
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| author | Vinod K. Bhardwaj Shweta Dhawan Sandeep Gupta |
| author_facet | Vinod K. Bhardwaj Shweta Dhawan Sandeep Gupta |
| author_sort | Vinod K. Bhardwaj |
| collection | DOAJ |
| description | We have generalized the notion of statistical boundedness by introducing the concept of f-statistical boundedness for scalar sequences where f is an unbounded modulus. It is shown that bounded sequences are precisely those sequences which are f-statistically bounded for every unbounded modulus f. A decomposition theorem for f-statistical convergence for vector valued sequences and a structure theorem for f-statistical boundedness have also been established. |
| format | Article |
| id | doaj-art-957d73feee004412bb75e338d9faadba |
| institution | Kabale University |
| issn | 1085-3375 1687-0409 |
| language | English |
| publishDate | 2016-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Abstract and Applied Analysis |
| spelling | doaj-art-957d73feee004412bb75e338d9faadba2025-02-03T05:48:08ZengWileyAbstract and Applied Analysis1085-33751687-04092016-01-01201610.1155/2016/21430182143018Density by Moduli and Statistical BoundednessVinod K. Bhardwaj0Shweta Dhawan1Sandeep Gupta2Department of Mathematics, Kurukshetra University, Kurukshetra 136119, IndiaDepartment of Mathematics, KVA DAV College for Women, Karnal 132001, IndiaDepartment of Mathematics, Arya P. G. College, Panipat 132103, IndiaWe have generalized the notion of statistical boundedness by introducing the concept of f-statistical boundedness for scalar sequences where f is an unbounded modulus. It is shown that bounded sequences are precisely those sequences which are f-statistically bounded for every unbounded modulus f. A decomposition theorem for f-statistical convergence for vector valued sequences and a structure theorem for f-statistical boundedness have also been established.http://dx.doi.org/10.1155/2016/2143018 |
| spellingShingle | Vinod K. Bhardwaj Shweta Dhawan Sandeep Gupta Density by Moduli and Statistical Boundedness Abstract and Applied Analysis |
| title | Density by Moduli and Statistical Boundedness |
| title_full | Density by Moduli and Statistical Boundedness |
| title_fullStr | Density by Moduli and Statistical Boundedness |
| title_full_unstemmed | Density by Moduli and Statistical Boundedness |
| title_short | Density by Moduli and Statistical Boundedness |
| title_sort | density by moduli and statistical boundedness |
| url | http://dx.doi.org/10.1155/2016/2143018 |
| work_keys_str_mv | AT vinodkbhardwaj densitybymoduliandstatisticalboundedness AT shwetadhawan densitybymoduliandstatisticalboundedness AT sandeepgupta densitybymoduliandstatisticalboundedness |