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ROUGH IDEAL CONVERGENCE

Year 2013, Volume: 42 Issue: 6, 633 - 640, 01.06.2013

Abstract

In this paper we extend the notion of rough convergence using theconcept of ideals which automatically extends the earlier notions ofrough convergence and rough statistical convergence. We define the setof rough ideal limit points and prove several results associated with thisset.

References

  • Aytar, S. The Rough Limit Set and the Core of a Real Sequence, Numer. Funct. Anal. Optimiz. 29, No. 3, 283–290, 2008.
  • Aytar, S. Rough Statistical Convergence, Numer. Funct. Anal. Optimiz. 29, No. 3, 291–303, 200 Cooke, R. G. Infinite Matrices and Sequence Spaces, (Dover Publ. Inc., New York, 1955).
  • Das, P. and Ghosal, S. K. Some further results on I-Cauchy sequences and condition(AP), Comp. Math. Appl. 59, 2597–2600, 2010.
  • Das, P., Pal, S. K. and Ghosal, S. K. Some further remarks on ideal summability in 2-normed spaces, Appl. Math. Lett. 24, 39–43, 2011.
  • Das, P., Savas, E. and Ghosal, S. K. On generalizations of certain summability methods using ideals, Appl. Math. Lett. 24, 1509–1514, 2011.
  • Demirci, K. I-limit superior and limit inferior, Math. Commun. 6, No.-2, 165–172, 2001.
  • Fast, H. Sur la convergence statistique, Colloq. Math. 2, 241–244, 1951.
  • Fridy, J. A. On Statistical Convergence, Analysis 5, 301–313, 1985.
  • Knopp, K. Zur theorie der limitierungsverfahern (Erste Mitteilung), Math. Z. 31, 97–127, 19 Kostyrko, P., ˇ Sal´ at, T. and Wilczy´ nski, W. I-Convergence, Real. Anal. Exchange 26, No. 2, 669–685, 2000/2001.
  • Kostyrko, P., M´ aˇ caz, M., ˇ Sal´ at, T. and Sleziak, M. I-Convergence and Extremal I-limit points, Math. Slovaca 55, No. 4, 443–454, 2005.
  • Lahiri, B. K. and Das, P. Further results on I-limit superior and I-limit inferior, Math. Commun. 8, 151–156, 2003.
  • Lahiri, B. K. and Das, P. I and I ∗ convergence in topological spaces, Math. Bohem. 130, No. 2, 153–160, 2005.
  • Pehlivan, S., Guncan, A. and Mammedov, M. Statistical cluster points of sequences in finite dimensional spaces, Czechoslovak Math. J. 54, No. 129, 95–102, 2004.
  • Phu, H. X. Rough Convergence in normed linear spaces, Numer. Funct. Anal. Optimiz. 22, 201–224, 2001.
  • Phu, H. X. Rough continuity of linear operators, Numer. Funct. Optimiz. 23, 139–146, 2000. Phu, H. X. Rough convergence in infinite dimensional normed spaces, Numer. Funct. Anal. Optimiz. 24, 285–301, 2003.
  • ˇ Sal´ at, T. On statistically convergent sequences of real numbers, Math. Slovaca 30, 139–150, 1980.
  • Savas, E. and Das, P. A generalized statistical convergence via ideals, Appl. Math. Lett. 24, 826–830, 2011.
  • Savas, E., Das, P. and Dutta, S. A note on strong matrix summability via ideals, Appl. Math. Lett. 25, 733–738, 2012.
  • Schoenberg, I. J. The integrability of certain functions and related summability methods, Amer. Math. Monthly 66, 361–375, 1959.
  • Steinhaus, H. Sur la convergence ordinaire et la convergence asymptotique, Colloq. Math. 2, 73–74, 1951.

ROUGH IDEAL CONVERGENCE

Year 2013, Volume: 42 Issue: 6, 633 - 640, 01.06.2013

Abstract

-

References

  • Aytar, S. The Rough Limit Set and the Core of a Real Sequence, Numer. Funct. Anal. Optimiz. 29, No. 3, 283–290, 2008.
  • Aytar, S. Rough Statistical Convergence, Numer. Funct. Anal. Optimiz. 29, No. 3, 291–303, 200 Cooke, R. G. Infinite Matrices and Sequence Spaces, (Dover Publ. Inc., New York, 1955).
  • Das, P. and Ghosal, S. K. Some further results on I-Cauchy sequences and condition(AP), Comp. Math. Appl. 59, 2597–2600, 2010.
  • Das, P., Pal, S. K. and Ghosal, S. K. Some further remarks on ideal summability in 2-normed spaces, Appl. Math. Lett. 24, 39–43, 2011.
  • Das, P., Savas, E. and Ghosal, S. K. On generalizations of certain summability methods using ideals, Appl. Math. Lett. 24, 1509–1514, 2011.
  • Demirci, K. I-limit superior and limit inferior, Math. Commun. 6, No.-2, 165–172, 2001.
  • Fast, H. Sur la convergence statistique, Colloq. Math. 2, 241–244, 1951.
  • Fridy, J. A. On Statistical Convergence, Analysis 5, 301–313, 1985.
  • Knopp, K. Zur theorie der limitierungsverfahern (Erste Mitteilung), Math. Z. 31, 97–127, 19 Kostyrko, P., ˇ Sal´ at, T. and Wilczy´ nski, W. I-Convergence, Real. Anal. Exchange 26, No. 2, 669–685, 2000/2001.
  • Kostyrko, P., M´ aˇ caz, M., ˇ Sal´ at, T. and Sleziak, M. I-Convergence and Extremal I-limit points, Math. Slovaca 55, No. 4, 443–454, 2005.
  • Lahiri, B. K. and Das, P. Further results on I-limit superior and I-limit inferior, Math. Commun. 8, 151–156, 2003.
  • Lahiri, B. K. and Das, P. I and I ∗ convergence in topological spaces, Math. Bohem. 130, No. 2, 153–160, 2005.
  • Pehlivan, S., Guncan, A. and Mammedov, M. Statistical cluster points of sequences in finite dimensional spaces, Czechoslovak Math. J. 54, No. 129, 95–102, 2004.
  • Phu, H. X. Rough Convergence in normed linear spaces, Numer. Funct. Anal. Optimiz. 22, 201–224, 2001.
  • Phu, H. X. Rough continuity of linear operators, Numer. Funct. Optimiz. 23, 139–146, 2000. Phu, H. X. Rough convergence in infinite dimensional normed spaces, Numer. Funct. Anal. Optimiz. 24, 285–301, 2003.
  • ˇ Sal´ at, T. On statistically convergent sequences of real numbers, Math. Slovaca 30, 139–150, 1980.
  • Savas, E. and Das, P. A generalized statistical convergence via ideals, Appl. Math. Lett. 24, 826–830, 2011.
  • Savas, E., Das, P. and Dutta, S. A note on strong matrix summability via ideals, Appl. Math. Lett. 25, 733–738, 2012.
  • Schoenberg, I. J. The integrability of certain functions and related summability methods, Amer. Math. Monthly 66, 361–375, 1959.
  • Steinhaus, H. Sur la convergence ordinaire et la convergence asymptotique, Colloq. Math. 2, 73–74, 1951.
There are 20 citations in total.

Details

Primary Language Turkish
Journal Section Mathematics
Authors

Sudip Kumar Pal This is me

Debraj Ch This is me

- - This is me

Sudipta Dutta This is me

Publication Date June 1, 2013
Published in Issue Year 2013 Volume: 42 Issue: 6

Cite

APA Pal, S. K., Ch, D., -, .-., Dutta, S. (2013). ROUGH IDEAL CONVERGENCE. Hacettepe Journal of Mathematics and Statistics, 42(6), 633-640.
AMA Pal SK, Ch D, -, Dutta S. ROUGH IDEAL CONVERGENCE. Hacettepe Journal of Mathematics and Statistics. June 2013;42(6):633-640.
Chicago Pal, Sudip Kumar, Debraj Ch, - -, and Sudipta Dutta. “ROUGH IDEAL CONVERGENCE”. Hacettepe Journal of Mathematics and Statistics 42, no. 6 (June 2013): 633-40.
EndNote Pal SK, Ch D, - -, Dutta S (June 1, 2013) ROUGH IDEAL CONVERGENCE. Hacettepe Journal of Mathematics and Statistics 42 6 633–640.
IEEE S. K. Pal, D. Ch, .-. -, and S. Dutta, “ROUGH IDEAL CONVERGENCE”, Hacettepe Journal of Mathematics and Statistics, vol. 42, no. 6, pp. 633–640, 2013.
ISNAD Pal, Sudip Kumar et al. “ROUGH IDEAL CONVERGENCE”. Hacettepe Journal of Mathematics and Statistics 42/6 (June 2013), 633-640.
JAMA Pal SK, Ch D, - -, Dutta S. ROUGH IDEAL CONVERGENCE. Hacettepe Journal of Mathematics and Statistics. 2013;42:633–640.
MLA Pal, Sudip Kumar et al. “ROUGH IDEAL CONVERGENCE”. Hacettepe Journal of Mathematics and Statistics, vol. 42, no. 6, 2013, pp. 633-40.
Vancouver Pal SK, Ch D, - -, Dutta S. ROUGH IDEAL CONVERGENCE. Hacettepe Journal of Mathematics and Statistics. 2013;42(6):633-40.