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Year 2016, Volume: 4 Issue: 4, 322 - 328, 31.12.2016

Dalip Singh Jamwal Rohini Jamwal Shivani Sharma

Abstract

References

  • V. Bala'z ̆, J. C ̆erven'ansky', P. Kostyrko, T. S ̆ala't, I-convergence and I-continuity of real functions, Faculty of Natural Sciences, Constantine the Philosoper University, Nitra, Acta Mathematical 5, 43-50, 2002.
  • N. Bourbaki, General Topology, Part (I) (transl.), Addison- Wesley, Reading (1966).
  • K. Demirci, I-limit superior and limit inferior, Math. Commun. 6 (2001), 165-172.
  • H. Fast, sur la convergence statistique, colloq. Math. 2 (1951), 241-244.
  • H. Halberstem, K. F. Roth, Sequences, Springer, New York, 1993.
  • P. Kostyrko, T.S ̆ala't, W. Wilczynski, I-convergence, Real Analysis, Exch. 26 (2) (2000/2001), 669-685.
  • P. Kostyrko, M. Mac ̆aj, T.S ̆ala't, M. Sleziak, I-convergence and extremal I-limit points, Math. Slovaca, 55 (4) (2005), 443-464.
  • B. K. Lahiri, P. Das, Further results on I-limit superior and I-limit inferior, Math. Commun., 8 (2003), 151-156.
  • B. K. Lahiri, P. Das, I and I^*-convergence in topological spaces, Math. Bohemica, 130 (2) (2005), 153-160.
  • B. K. Lahiri, P. Das, I and I^*-convergence of nets, Real Analysis Exchange, 33 (2) (2007/2008), 431-442.
  • M. Mac ̆aj, T.S ̆ala't, Statistical convergence of subsequences of a given sequence, Math. Bohemica, 126 (2001), 191-208.
  • M. Mursaleen and A. Alotaibi, On I–convergence in random 2–normed spaces, Math. Slovaca, 61(6) (2011) 933–940.
  • M. Mursaleen and S. A. Mohiuddine, On ideal convergence of double sequences in probabilistic normed spaces, Math. Reports, 12(62)(4) (2010) 359-371.
  • M. Mursaleen and S. A. Mohiuddine, On ideal convergence in probabilistic normed spaces, Math. Slovaca, 62(1) (2012) 49-62.
  • M. Mursaleen, S. A. Mohiuddine and O. H. H. Edely, On the ideal convergence of double sequences in intuitionistic fuzzy normed spaces, Comput. Math. Appl., 59 (2010) 603-611.
  • I. Niven, H. S. Zuckerman, An introduction to the theory of numbers, 4th Ed., John Wiley, New York, 1980.
  • T.S ̆ala't, On statistically convergent sequences of real numbers, Mathematical Slovaca, 30 (1980), No. 2, 139-150.
  • T.S ̆ala't, B. C. Tripathy, M. Ziman, On I-convergence field, Italian J. of Pure Appl. Math. 17 (2005), 45-54.
  • A.Sahiner, M. Gürdal, S. Saltan and H. Gunawan, Ideal convergence in 2-normed spaces, Taiwanese J. Math., 11(5) (2007), 1477-1484.
  • I. J. Schoenberg, The integrability of certain function and related summability methods, Am. Math. Mon. 66 (1959), 361-375.
  • S. Willard, General Topology, Addison-Wesley Pub. Co. 1970.

I-convergence of filters

Year 2016, Volume: 4 Issue: 4, 322 - 328, 31.12.2016

Dalip Singh Jamwal Rohini Jamwal Shivani Sharma

Abstract

In this paper, we have introduced the idea of I-convergence of filters and studied its various properties. We have proved the necessary and sufficient condition for a filter to be I-convergent.

Keywords

Ideal filters ideal convergence admissible ideal

References

  • V. Bala'z ̆, J. C ̆erven'ansky', P. Kostyrko, T. S ̆ala't, I-convergence and I-continuity of real functions, Faculty of Natural Sciences, Constantine the Philosoper University, Nitra, Acta Mathematical 5, 43-50, 2002.
  • N. Bourbaki, General Topology, Part (I) (transl.), Addison- Wesley, Reading (1966).
  • K. Demirci, I-limit superior and limit inferior, Math. Commun. 6 (2001), 165-172.
  • H. Fast, sur la convergence statistique, colloq. Math. 2 (1951), 241-244.
  • H. Halberstem, K. F. Roth, Sequences, Springer, New York, 1993.
  • P. Kostyrko, T.S ̆ala't, W. Wilczynski, I-convergence, Real Analysis, Exch. 26 (2) (2000/2001), 669-685.
  • P. Kostyrko, M. Mac ̆aj, T.S ̆ala't, M. Sleziak, I-convergence and extremal I-limit points, Math. Slovaca, 55 (4) (2005), 443-464.
  • B. K. Lahiri, P. Das, Further results on I-limit superior and I-limit inferior, Math. Commun., 8 (2003), 151-156.
  • B. K. Lahiri, P. Das, I and I^*-convergence in topological spaces, Math. Bohemica, 130 (2) (2005), 153-160.
  • B. K. Lahiri, P. Das, I and I^*-convergence of nets, Real Analysis Exchange, 33 (2) (2007/2008), 431-442.
  • M. Mac ̆aj, T.S ̆ala't, Statistical convergence of subsequences of a given sequence, Math. Bohemica, 126 (2001), 191-208.
  • M. Mursaleen and A. Alotaibi, On I–convergence in random 2–normed spaces, Math. Slovaca, 61(6) (2011) 933–940.
  • M. Mursaleen and S. A. Mohiuddine, On ideal convergence of double sequences in probabilistic normed spaces, Math. Reports, 12(62)(4) (2010) 359-371.
  • M. Mursaleen and S. A. Mohiuddine, On ideal convergence in probabilistic normed spaces, Math. Slovaca, 62(1) (2012) 49-62.
  • M. Mursaleen, S. A. Mohiuddine and O. H. H. Edely, On the ideal convergence of double sequences in intuitionistic fuzzy normed spaces, Comput. Math. Appl., 59 (2010) 603-611.
  • I. Niven, H. S. Zuckerman, An introduction to the theory of numbers, 4th Ed., John Wiley, New York, 1980.
  • T.S ̆ala't, On statistically convergent sequences of real numbers, Mathematical Slovaca, 30 (1980), No. 2, 139-150.
  • T.S ̆ala't, B. C. Tripathy, M. Ziman, On I-convergence field, Italian J. of Pure Appl. Math. 17 (2005), 45-54.
  • A.Sahiner, M. Gürdal, S. Saltan and H. Gunawan, Ideal convergence in 2-normed spaces, Taiwanese J. Math., 11(5) (2007), 1477-1484.
  • I. J. Schoenberg, The integrability of certain function and related summability methods, Am. Math. Mon. 66 (1959), 361-375.
  • S. Willard, General Topology, Addison-Wesley Pub. Co. 1970.
There are 21 citations in total.

Details

Primary Language English
Journal Section Articles
Authors

Dalip Singh Jamwal This is me

Rohini Jamwal This is me

Shivani Sharma This is me

Publication Date December 31, 2016
Published in Issue Year 2016 Volume: 4 Issue: 4

Cite

APA Jamwal, D. S., Jamwal, R., & Sharma, S. (2016). I-convergence of filters. New Trends in Mathematical Sciences, 4(4), 322-328.
AMA Jamwal DS, Jamwal R, Sharma S. I-convergence of filters. New Trends in Mathematical Sciences. December 2016;4(4):322-328.
Chicago Jamwal, Dalip Singh, Rohini Jamwal, and Shivani Sharma. “I-Convergence of Filters”. New Trends in Mathematical Sciences 4, no. 4 (December 2016): 322-28.
EndNote Jamwal DS, Jamwal R, Sharma S (December 1, 2016) I-convergence of filters. New Trends in Mathematical Sciences 4 4 322–328.
IEEE D. S. Jamwal, R. Jamwal, and S. Sharma, “I-convergence of filters”, New Trends in Mathematical Sciences, vol. 4, no. 4, pp. 322–328, 2016.
ISNAD Jamwal, Dalip Singh et al. “I-Convergence of Filters”. New Trends in Mathematical Sciences 4/4 (December 2016), 322-328.
JAMA Jamwal DS, Jamwal R, Sharma S. I-convergence of filters. New Trends in Mathematical Sciences. 2016;4:322–328.
MLA Jamwal, Dalip Singh et al. “I-Convergence of Filters”. New Trends in Mathematical Sciences, vol. 4, no. 4, 2016, pp. 322-8.
Vancouver Jamwal DS, Jamwal R, Sharma S. I-convergence of filters. New Trends in Mathematical Sciences. 2016;4(4):322-8.