I-statistically pre-Cauchy double sequences

المؤلفون

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

DOI:

https://doi.org/10.14419/gjma.v2i4.3135

الكلمات المفتاحية:

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

الملخص

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.

المراجع

  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 Unpublished; http://thales.doa.fmph.uniba.sk/macaj/ICON.pdf.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.

التنزيلات

الملفات الإضافية

منشور

28-10-2014

إصدار

القسم

Articles

كيفية الاقتباس

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