Remarks on statistical and -convergence of series
Jaroslav Červeňanský; Tibor Šalát; Vladimír Toma
Mathematica Bohemica (2005)
- Volume: 130, Issue: 2, page 177-184
- ISSN: 0862-7959
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topČerveňanský, Jaroslav, Šalát, Tibor, and Toma, Vladimír. "Remarks on statistical and $I$-convergence of series." Mathematica Bohemica 130.2 (2005): 177-184. <http://eudml.org/doc/249600>.
@article{Červeňanský2005,
abstract = {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.},
author = {Červeňanský, Jaroslav, Šalát, Tibor, Toma, Vladimír},
journal = {Mathematica Bohemica},
keywords = {statistical convergence; $I$-convergence; $I$-convergent series; statistical convergence},
language = {eng},
number = {2},
pages = {177-184},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Remarks on statistical and $I$-convergence of series},
url = {http://eudml.org/doc/249600},
volume = {130},
year = {2005},
}
TY - JOUR
AU - Červeňanský, Jaroslav
AU - Šalát, Tibor
AU - Toma, Vladimír
TI - Remarks on statistical and $I$-convergence of series
JO - Mathematica Bohemica
PY - 2005
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 130
IS - 2
SP - 177
EP - 184
AB - 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.
LA - eng
KW - statistical convergence; $I$-convergence; $I$-convergent series; statistical convergence
UR - http://eudml.org/doc/249600
ER -
References
top- The uniform density of sets of integers and Fermat’s Last Theorem, C. R. Math. Acad. Sci., R. Can. 12 (1990), 1–6. (1990) MR1043085
- The statistical and strong p-Cesáro convergence of sequences, Analysis 8 (1988), 47–63. (1988) Zbl0653.40001MR0954458
- Two valued measures and summability, Analysis 10 (1990), 373–385. (1990) Zbl0726.40009MR1085803
- Statistical convergence of infinite series, Czechoslovak Math. J. (2003). (2003) MR2018844
- Sur la convergence statistique, Coll. Math. 2 (1951), 242–244. (1951) Zbl0044.33605MR0048548
- Sequences I, Oxford, Clarendon Press, 1966. (1966)
- 10.1090/S0002-9939-00-05891-3, Proc. Amer. Math. Soc. 129 (2001), 2647–2654. (2001) MR1838788DOI10.1090/S0002-9939-00-05891-3
- -convergence, Real. Anal. Exchange 26 (2000 –2001), 669–686. (2000 –2001) MR1844385
- Convergence of subseries of the harmonic series and asymptotic densities of sets of positive integers, Publ. Inst. Math. (Beograd) 50 (1991), 60–70. (1991) MR1252159
- On statistically convergent sequences of real numbers, Math. Slov. 30 (1980), 139–150. (1980) MR0587239
- Infinite Series, Academia, Praha, 1974. (Slovak) (1974)
- 10.2307/2308747, Amer. Math. Monthly 66 (1959), 361–375. (1959) Zbl0089.04002MR0104946DOI10.2307/2308747
- On statistically convergent series, Punjab. Univ. J. Math. 32 (1999), 1–8. (1999) Zbl0966.40003MR1778259
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