| Title:
|
Statistical cluster points of sequences in finite dimensional spaces (English) |
| Author:
|
Pehlivan, S. |
| Author:
|
Güncan, A. |
| Author:
|
Mamedov, M. A. |
| Language:
|
English |
| Journal:
|
Czechoslovak Mathematical Journal |
| ISSN:
|
0011-4642 (print) |
| ISSN:
|
1572-9141 (online) |
| Volume:
|
54 |
| Issue:
|
1 |
| Year:
|
2004 |
| Pages:
|
95-102 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
In this paper we study the set of statistical cluster points of sequences in $m$-dimensional spaces. We show that some properties of the set of statistical cluster points of the real number sequences remain in force for the sequences in $m$-dimensional spaces too. We also define a notion of $\Gamma $-statistical convergence. A sequence $x$ is $\Gamma $-statistically convergent to a set $C$ if $C$ is a minimal closed set such that for every $\epsilon > 0 $ the set $ \lbrace k\:\rho (C, x_k ) \ge \epsilon \rbrace $ has density zero. It is shown that every statistically bounded sequence is $\Gamma $-statistically convergent. Moreover if a sequence is $\Gamma $-statistically convergent then the limit set is a set of statistical cluster points. (English) |
| Keyword:
|
compact sets |
| Keyword:
|
natural density |
| Keyword:
|
statistically bounded sequence |
| Keyword:
|
statistical cluster point |
| MSC:
|
11B05 |
| MSC:
|
40A05 |
| idZBL:
|
Zbl 1045.40004 |
| idMR:
|
MR2040222 |
| . |
| Date available:
|
2009-09-24T11:10:02Z |
| Last updated:
|
2020-07-03 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/127867 |
| . |
| 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] M. A. Mamedov and S. Pehlivan: Statistical cluster points and Turnpike theorem in nonconvex problems.J. Math. Anal. Appl. 256 (2001), 686–693. MR 1821765, 10.1006/jmaa.2000.7061 |
| Reference:
|
[9] T. Šalát: On statistically convergent sequences of real numbers.Math. Slovaca 30 (1980), 139–150. MR 0587239 |
| . |
