Skip to content
GJMA Global Journal of Mathematical Analysis E-ISSN 2307-9002

I-statistically pre-Cauchy double sequences

Authors and Affiliations

  • Ulas Yamanci Suleyman Demirel University, Department of Mathematics, 32260, Isparta, Turkey
  • Mehmet Gurdal

About this article

DOI
https://doi.org/10.14419/gjma.v2i4.3135
Received
09-07-2014
Accepted
10-08-2014
Published
28-10-2014
Views
1012
Downloads
541
Download PDF

Abstract

In the present paper we are concerned with I-statistically pre-Cauchy double sequences in line of of Das et al. [5]. Particularly, we prove that for double sequences, I-statistical convergence implies I-statistical pre-Cauchy condition and examine some main properties of these concepts.

Keywords

  • Double sequences
  • Ideal
  • Filter
  • I-statistical convergence
  • I-statistical pre-Cauchy.

References

  1. C. Belen, M. Yildirim, On generalized statistical convergence of double sequences via ideals, Ann. Univ. Ferrara Sez. VII Sci. Mat., 58(1)(2012) 11-20.
  2. J. Connor, J. Fridy, and J. Kline, Statistically Pre-Cauchy Sequences, Analysis, 14(1994) 311-317.
  3. P. Das, S. Ghosal, Some further results on I-Cauchy sequences and condition (AP), Comput. Math. Appl., 59(2010) 2597-2600.
  4. P. Das, E. Sava?, S.Kr. Ghosal, On generalizations of certain summability methods using ideals, Appl. Math. Lett., 24(2011) 1509-1514.
  5. P. Das, E. Sava?, On I-statistically pre-Cauchy sequences, Taiwanese J. Math., 18(1)(2014) 115-126.
  6. H. Fast, Sur la convergence statistique, Colloq. Math., 2(1951), 241-244.
  7. A.R. Freedman, J.J. Sember, Densities and summability, Pacitic J. Math., 95(1981) 10-11.
  8. J.A. Fridy, On statistical convergence, Analysis, 5(1985) 301-313.
  9. J.A. Fridy, M.K. Khan, Tauberian theorems via statistical convergence, J. Math. Anal. Appl., 228 (1998) 73-95.
  10. M. Grdal, Statistically pre-Cauchy sequences and bounded moduli, Acta Comm. Tartu. Math., 7(2003) 3-7.
  11. M. Grdal, S. Pehlivan, The statistical convergence in 2-Banach spaces, Thai. J. Math., 2(1)(2004) 107-113.
  12. M. Grdal, I. A?k, On I-cauchy sequences in 2-normed spaces, Math. Inequal. Appl., 11(2)(2008) 349-354.
  13. M. Grdal, A. ?ahiner, Extremal I-limit points of double sequences, Appl. Math. E-Notes, 8 (2008) 131-137.
  14. M. Grdal, A. ?ahiner, I. A?k, Approximation theory in 2-Banach spaces, Nonlinear Analysis, 71(5-6)(2009) 1654-1661.
  15. P. Kostyrko, M. Macaj, T. Salat, Statistical convergence and I-convergence, 1999. Unpublished; http://thales.doa.fmph.uniba.sk/macaj/ICON.pdf.
  16. P. Kostyrko, T. Salat, W. Wilczynki, I-convergence, Real Anal. Exchange, 26(2)(2000-2001) 669-685.
  17. H.I. Miller, A measure theoretical subsequence characterization of statistical convergence, Trans. Amer. Math. Soc., 347 (1995) 1811-1819.
  18. M. Mursaleen, O.H. Edely, Statistical convergence of double sequences, J. Math. Anal. Appl., 288(2003) 223-231.
  19. M. Mursaleen, S.A. Mohiuddine, On Ideal Convergence of Double Sequences in Probabilistic Normed Spaces, Math. Reports, 12(62)(2010) 359-371.
  20. A. Nabiev, S. Pehlivan, M. Grdal, On I-Cauchy sequences, Taiwanese J. Math., 11(2)(2007) 569-576.
  21. E. Sava?, P. Das, A generalized statistical convergence via ideals, Appl. Math. Lett., 24(2011) 826-830.
  22. E. Sava?, S.A. Mohiuddine, I-statistically convergent double sequences in probabilistic normed spaces, Math. Slovaca, 62(1) (2012) 99-108.
  23. E. Sava?, M. Grdal, Certain summability methods in intuitionistic fuzzy normed spaces, Journal of Intelligent and Fuzzy Systems, 27(4)(2014) 1621-1629.
  24. A. ?ahiner, M. Grdal, S. Saltan, H. Gunawan, Ideal convergence in 2-normed spaces, Taiwanese J. Math., 11(5)(2007) 1477-1484.
  25. H. Steinhaus, Sur la convergence ordinaire et la convergence asymptotique, Colloq. Math., 2(1951) 73-74. B.C.
  26. Tripathy, On I-convergent double sequences, Soochow J. Math., 31(4)(2005) 549-560.
  27. U. Yamanc?, M. Grdal, I-statistical convergence in 2-normed space, Arab Journal of Mathematical Sciences, 20(1)(2014) 41-47.
  28. A. Zygmund, Trigonometric Series, second ed., Cambridge Univ. Press, 1979.


How to Cite

Yamanci, U., & Gurdal, M. (2014). I-statistically pre-Cauchy double sequences. Global Journal of Mathematical Analysis, 2(4), 297-303. https://doi.org/10.14419/gjma.v2i4.3135

Related Articles

Additional Files