A-Statistical Convergence of Subsequence of Double Sequences

Harry I. Miller

Bollettino dell'Unione Matematica Italiana (2007)

  • Volume: 10-B, Issue: 3, page 727-739
  • ISSN: 0392-4033

Abstract

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The concept of statistical convergence of a sequence was first introduced by H. Fast [7] in 1951. Recently, in the literature, the concept of statistical convergence of double sequences has been studied. The main result in this paper is a theorem that gives meaning to the statement: s = s i j converges statistically A to L if and only if "most" of the "subsequences" of s converge to L in the ordinary sense. The results presented here are analogue of theorems in [12], [13] and [6] and are concerned with A statistical convergence, first introduced by Freedman and Sember [8]. Other related problems are considered.

How to cite

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Miller, Harry I.. "A-Statistical Convergence of Subsequence of Double Sequences." Bollettino dell'Unione Matematica Italiana 10-B.3 (2007): 727-739. <http://eudml.org/doc/290396>.

@article{Miller2007,
abstract = {The concept of statistical convergence of a sequence was first introduced by H. Fast [7] in 1951. Recently, in the literature, the concept of statistical convergence of double sequences has been studied. The main result in this paper is a theorem that gives meaning to the statement: $s=\{s_\{ij\}\}$ converges statistically $A$ to $L$ if and only if "most" of the "subsequences" of $s$ converge to $L$ in the ordinary sense. The results presented here are analogue of theorems in [12], [13] and [6] and are concerned with $A$ statistical convergence, first introduced by Freedman and Sember [8]. Other related problems are considered.},
author = {Miller, Harry I.},
journal = {Bollettino dell'Unione Matematica Italiana},
language = {eng},
month = {10},
number = {3},
pages = {727-739},
publisher = {Unione Matematica Italiana},
title = {A-Statistical Convergence of Subsequence of Double Sequences},
url = {http://eudml.org/doc/290396},
volume = {10-B},
year = {2007},
}

TY - JOUR
AU - Miller, Harry I.
TI - A-Statistical Convergence of Subsequence of Double Sequences
JO - Bollettino dell'Unione Matematica Italiana
DA - 2007/10//
PB - Unione Matematica Italiana
VL - 10-B
IS - 3
SP - 727
EP - 739
AB - The concept of statistical convergence of a sequence was first introduced by H. Fast [7] in 1951. Recently, in the literature, the concept of statistical convergence of double sequences has been studied. The main result in this paper is a theorem that gives meaning to the statement: $s={s_{ij}}$ converges statistically $A$ to $L$ if and only if "most" of the "subsequences" of $s$ converge to $L$ in the ordinary sense. The results presented here are analogue of theorems in [12], [13] and [6] and are concerned with $A$ statistical convergence, first introduced by Freedman and Sember [8]. Other related problems are considered.
LA - eng
UR - http://eudml.org/doc/290396
ER -

References

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  9. FRIDY, J., On statistical convergence, Analysis, 5 (1985), 301-313. Zbl0588.40001MR816582DOI10.1524/anly.1985.5.4.301
  10. FRIDY, J. - ORHAN, C., Lacunary statistical convergence, Pacific J. Math., 160 (1993), 43-51. Zbl0794.60012MR1227502
  11. FRIDY, J. - ORHAN, C., Lacunary statistical summability, J. Math. Anal. Appl., 173 (1993). Zbl0786.40004MR1209334DOI10.1006/jmaa.1993.1082
  12. MILLER, H. I., Measure theoretical subsequence characterization of statistical convergence, Trans. Amer. Math. Soc., 347 (5) (1995), 1811-1819. Zbl0830.40002MR1260176DOI10.2307/2154976
  13. MILLER, H. I. - ORHAN, C., On almost convergent and statistically convergent subsequences, Acta Math. Hung., 93 (1-2) (2001), 135-151. Zbl0989.40002MR1924673DOI10.1023/A:1013877718406
  14. MÓRICZ, F., Statistical convergence of multiple sequences, Arch. Math. (Basel), 81 (2003), 82-89. MR2002719DOI10.1007/s00013-003-0506-9

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