The sets of \((\alpha, \beta)\)-statistically convergent and \((\alpha, \beta)\)-statistically bounded sequences of order \(\gamma\) defined by modulus functions (Q6562342)
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scientific article; zbMATH DE number 7871643
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | The sets of \((\alpha, \beta)\)-statistically convergent and \((\alpha, \beta)\)-statistically bounded sequences of order \(\gamma\) defined by modulus functions |
scientific article; zbMATH DE number 7871643 |
Statements
The sets of \((\alpha, \beta)\)-statistically convergent and \((\alpha, \beta)\)-statistically bounded sequences of order \(\gamma\) defined by modulus functions (English)
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26 June 2024
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The authors introduce \((\alpha, \beta)\)-statistical convergence (statistical boundedness) of order \(\gamma\) by using unbounded modulus functions in metric spaces. Every convergent sequence in a metric space $(X,d)$ is \((\alpha, \beta)\)-statistical convergent for any unbounded modulus $f$. But the converse does not have to be true. Also this new concept is characterized. In the meanwhile the relationship between these concepts according to order are studied.
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modulus function
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\((\alpha, \beta)\)-density
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\((\alpha, \beta)\)-statistical convergence
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\((\alpha, \beta)\)-statistical boundedness
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