| Title:
|
Two valued measure and summability of double sequences (English) |
| Author:
|
Das, Pratulananda |
| Author:
|
Bhunia, Santanu |
| Language:
|
English |
| Journal:
|
Czechoslovak Mathematical Journal |
| ISSN:
|
0011-4642 (print) |
| ISSN:
|
1572-9141 (online) |
| Volume:
|
59 |
| Issue:
|
4 |
| Year:
|
2009 |
| Pages:
|
1141-1155 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
In this paper, following the methods of Connor \cite {connor}, we extend the idea of statistical convergence of a double sequence (studied by Muresaleen and Edely \cite {moe}) to $\mu $-statistical convergence and convergence in $\mu $-density using a two valued measure $\mu $. We also apply the same methods to extend the ideas of divergence and Cauchy criteria for double sequences. We then introduce a property of the measure $\mu $ called the (APO$_2$) condition, inspired by the (APO) condition of Connor \cite {jc}. We mainly investigate the interrelationships between the two types of convergence, divergence and Cauchy criteria and ultimately show that they become equivalent if and only if the measure $\mu $ has the condition (APO$_2$). (English) |
| Keyword:
|
double sequences |
| Keyword:
|
$\mu $-statistical convergence |
| Keyword:
|
divergence and Cauchy criteria |
| Keyword:
|
convergence |
| Keyword:
|
divergence and Cauchy criteria in $\mu $-density |
| Keyword:
|
condition (APO$_2)$ |
| MSC:
|
40A05 |
| MSC:
|
40A30 |
| MSC:
|
40B05 |
| idZBL:
|
Zbl 1224.40009 |
| idMR:
|
MR2563584 |
| . |
| Date available:
|
2010-07-20T16:09:48Z |
| Last updated:
|
2020-07-03 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/140543 |
| . |
| Reference:
|
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| Reference:
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| Reference:
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