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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Bibliographic Details
Published in:Quaestiones mathematicae Vol. 37; no. 4; pp. 525 - 530
Main Authors: Aizpuru, A., Listán-García, M.C., Rambla-Barreno, F.
Format: Journal Article
Language:English
Published: Grahamstown Taylor & Francis 01.01.2014
Taylor & Francis Ltd
Subjects:
Convergence
Density
modulus function
Primary 40A35
Secondary 46A45
statistical convergence
ISSN:1607-3606, 1727-933X
Online Access:Get full text
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Summary: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.
Bibliography:SourceType-Scholarly Journals-1
ObjectType-Feature-1
content type line 14
ISSN:1607-3606
1727-933X
DOI:10.2989/16073606.2014.981683