Remarks on statistical and I -convergence of series

Jaroslav Červeňanský; Tibor Šalát; Vladimír Toma

Mathematica Bohemica (2005)

  • Volume: 130, Issue: 2, page 177-184
  • ISSN: 0862-7959

Abstract

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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.

How to cite

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Červeňanský, 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

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