| Title:
|
Some remarks on $I$-faster convergent infinite series (English) |
| Author:
|
Matejíčka, Ladislav |
| Language:
|
English |
| Journal:
|
Mathematica Bohemica |
| ISSN:
|
0862-7959 (print) |
| ISSN:
|
2464-7136 (online) |
| Volume:
|
134 |
| Issue:
|
3 |
| Year:
|
2009 |
| Pages:
|
275-284 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
A structure of terms of $I$-faster convergent series is studied in the paper. Necessary and sufficient conditions for the existence of $I$-faster convergent series with different types of their terms are proved. Some consequences are discussed. (English) |
| Keyword:
|
$I$-convergence |
| Keyword:
|
$I$-faster convergent series |
| Keyword:
|
terms of $I$-convergent series |
| MSC:
|
40A10 |
| MSC:
|
65B10 |
| idZBL:
|
Zbl 1212.65002 |
| idMR:
|
MR2561306 |
| DOI:
|
10.21136/MB.2009.140661 |
| . |
| Date available:
|
2010-07-20T18:03:06Z |
| Last updated:
|
2020-07-29 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/140661 |
| . |
| Reference:
|
[1] Činčura, J., Sleziak, M., Šalát, T., Toma, V.: Sets of statistical cluster points and $I$-cluster points.Real Anal. Exchange 30 (2005), 565-580. MR 2177419 |
| Reference:
|
[2] Dawson, D. F.: Matrix summability over certain classes of sequences ordered with respect to rate of convergence.Pacific J. Math. 24 (1968), 51-56. Zbl 0157.11202, MR 0222508, 10.2140/pjm.1968.24.51 |
| Reference:
|
[3] Dindoš, M., Šalát, T., Toma, V.: Statistical convergence of infinite series.Czech. Math. J. 53 (2003), 989-1000. Zbl 1080.40500, MR 2018844, 10.1023/B:CMAJ.0000024535.89828.e8 |
| Reference:
|
[4] Filipów, R., Reclaw, I., N. Mro' zek, Szuca, P.: Ideal convergence of bounded sequences.J. Symbolic Logic 72 (2007), 501-512. MR 2320288, 10.2178/jsl/1185803621 |
| Reference:
|
[5] Holý, D., Matejíčka, L., Pinda, Ľ.: On faster convergent infinite series.International Journal of Mathematics and Mathematical Sciences, ISSN 0161-1712, Vol. 2008, Article ID 753632 (2008). Zbl 1141.40001, MR 2407165, 10.1155/2008/753632 |
| Reference:
|
[6] Holý, D., Matejíčka, L., Pinda, Ľ.: Some remarks on faster convergent infinite series.Preprint. |
| Reference:
|
[7] Keagy, T. A., Ford, W. F.: Acceleration by subsequence transformation.Pacific J. Math. 132 (1988), 357-362. MR 0934175, 10.2140/pjm.1988.132.357 |
| Reference:
|
[8] Kostyrko, P., Šalát, T., Wilczyński, W.: $\Bbb I$-Convergence.Real Anal. Exchange 26 (2000)/2001 669-686. MR 1844385 |
| Reference:
|
[9] Kostyrko, P., Mačaj, M., Šalát, T., Sleziak, M.: $\Bbb I$-Convergence and extremal $\Bbb I$-limit points.Math. Slovaca 55 (2005). MR 2181783 |
| Reference:
|
[10] Salzer, H. E.: A simple method for summing certain slowly convergent series.J. Math. Physics 33 (1955), 356-359. Zbl 0065.10801, MR 0068315, 10.1002/sapm1954331356 |
| Reference:
|
[11] Smith, D. A., Ford, W. F.: Acceleration of linear and logarithmic convergence.Siam J. Numer. Anal. 16 (1979), 223-240. Zbl 0407.65002, MR 0526486, 10.1137/0716017 |
| Reference:
|
[12] Šalát, T., Toma, V.: A classical Olivier's theorem and statistical convergence.Annales Mathématiques Blaise Pascal 10 (2003), 305-313. Zbl 1061.40001, MR 2031274, 10.5802/ambp.179 |
| Reference:
|
[13] Tripathy, B. C.: On statistical convergence.Proc. Estonian Acad. Sci. Phys. Math. 47 (1998), 299-303. Zbl 0961.40002, MR 1671445 |
| Reference:
|
[14] Wimp, J.: Some transformations of monotone sequences.Math. Comput. 26 (1972), 251-254. Zbl 0257.40001, MR 0303674, 10.1090/S0025-5718-1972-0303674-X |
| . |
