| Title:
|
Remarks on statistical and $I$-convergence of series (English) |
| Author:
|
Červeňanský, J. |
| Author:
|
Šalát, T. |
| Author:
|
Toma, V. |
| Language:
|
English |
| Journal:
|
Mathematica Bohemica |
| ISSN:
|
0862-7959 (print) |
| ISSN:
|
2464-7136 (online) |
| Volume:
|
130 |
| Issue:
|
2 |
| Year:
|
2005 |
| Pages:
|
177-184 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
In this paper we investigate the relationship between the statistical (or generally $I$-convergence) of a series and the usual convergence of its subseries. We also give a counterexample which shows that Theorem 1 of the paper by B. C. Tripathy “On statistically convergent series”, Punjab. Univ. J. Math. 32 (1999), 1–8, is not correct. (English) |
| Keyword:
|
statistical convergence |
| Keyword:
|
$I$-convergence |
| Keyword:
|
$I$-convergent series |
| MSC:
|
40A05 |
| MSC:
|
54A20 |
| idZBL:
|
Zbl 1110.40001 |
| idMR:
|
MR2148651 |
| DOI:
|
10.21136/MB.2005.134134 |
| . |
| Date available:
|
2009-09-24T22:19:53Z |
| Last updated:
|
2020-07-29 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/134134 |
| . |
| Reference:
|
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| Reference:
|
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| Reference:
|
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| Reference:
|
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| Reference:
|
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| Reference:
|
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| Reference:
|
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| Reference:
|
[8] P. Kostyrko, T. Šalát, W. Wilczyński: $I$-convergence.Real. Anal. Exchange 26 (2000 –2001), 669–686. MR 1844385 |
| Reference:
|
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| Reference:
|
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| Reference:
|
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| Reference:
|
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| Reference:
|
[13] B. C. Tripathy: On statistically convergent series.Punjab. Univ. J. Math. 32 (1999), 1–8. Zbl 0966.40003, MR 1778259 |
| . |
