Density by moduli and statistical convergence
By using modulus functions we introduce a new concept of density for sets of natural numbers. Consequently, we obtain a generalization of the notion of statistical convergence which is studied and characterized. As an application, we prove that the ordinary convergence is equivalent to the module st...
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| Vydané v: | Quaestiones mathematicae Ročník 37; číslo 4; s. 525 - 530 |
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| Hlavní autori: | , , |
| Médium: | Journal Article |
| Jazyk: | English |
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Grahamstown
Taylor & Francis
01.01.2014
Taylor & Francis Ltd |
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| ISSN: | 1607-3606, 1727-933X |
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| Abstract | By using modulus functions we introduce a new concept of density for sets of natural numbers. Consequently, we obtain a generalization of the notion of statistical convergence which is studied and characterized. As an application, we prove that the ordinary convergence is equivalent to the module statistical conver- gence for every unbounded modulus function. |
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| AbstractList | By using modulus functions we introduce a new concept of density for sets of natural numbers. Consequently, we obtain a generalization of the notion of statistical convergence which is studied and characterized. As an application, we prove that the ordinary convergence is equivalent to the module statistical conver- gence for every unbounded modulus function. |
| Author | Listán-García, M.C. Rambla-Barreno, F. Aizpuru, A. |
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| Cites_doi | 10.4153/CJM-1973-102-9 10.4064/cm-2-2-98-108 10.2969/jmsj/00510029 10.2140/pjm.1981.95.293 10.4064/cm-2-3-4-241-244 10.1524/anly.1985.5.4.301 10.1006/jmaa.2000.6725 10.1017/S0305004100066883 |
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| References | Steinhaus H. (cit0011) 1951; 2 Fast H. (cit0003) 1951; 2 cit0010 cit0008 Kolk E. (cit0006) 1991; 928 Pehlivan S. (cit0009) 1994; 20 cit0007 cit0004 cit0005 cit0002 |
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| SubjectTerms | Convergence Density modulus function Primary 40A35 Secondary 46A45 statistical convergence |
| Title | Density by moduli and statistical convergence |
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