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On weighted weak statistical convergence

Year 2018, Volume: 6 Issue: 2, 194 - 199, 15.10.2018

Abstract

The purpose of the present work is to introduce extended notion of weak statistical convergence on normed spaces. Furthermore, some certain properties of this mode of convergence are given.



References

  • [1] A. Zygmund, Trigonometric Series, Cambridge University Press, New York, NY, USA, 1959.
  • [2] H. Fast, Sur la convergence statistique, Colloq. Math. 2 (1951) 241-244.
  • [3] H. Steinhaus, Sur la convergence ordinaire et la convergence asymptotique, Colloq. Math. 2 (1951) 73-74.
  • [4] A. R. Freedman, J. J. Sember, M. Raphael, Some Ces`aro-type summability spaces, Proc. Lond. Math. Soc. 37(3) (1978) 508-520.
  • [5] D. Rath, B. C. Tripathy, On statistically convergent and statistically Cauchy sequences, Indian J. Pure. Appl. Math. 25(4) (1994) 381-386. [6] T. ˇ Sal´at, On statistically convergent sequences of real numbers, Math. Slovaca 30 (1980) 139-150.
  • [7] J. Connor, M. Ganichev, V. Kadets, A characterization of Banach spaces with separable duals via weak statistical convergence, J. Math. Anal. Appl. 244 (2000) 251-261.
  • [8] V.K. Bhardwaj, I. Bala, On weak statistical convergence, Int. J. Math. Math. Sci. Art. ID 38530, (2007) 9 pp.
  • [9] Meenakshi, M. S. Saroa , V. Kumar, Weak statistical convergence defined by de la Vall´ee-Poussin mean, Bull. Calcutta Math. Soc. 106 no.3 (2014) 215-224
  • [10] V. Karakaya, T. A. Chishti, Weighted statistical convergence, Iran. J. Sci. Technol. Trans. A Sci. 33 (2009) 219-223.
  • [11] M. K¨uc¸ ¨ukaslan, Weighted statistical convergence, International Journal of Science and Technology, 2 (2012) 2-10.
  • [12] M. Mursaleen, V. Karakaya, M. Ert¨urk, F. G¨ursoy, Weighted statistical convergence and its application to Korovkin type aprroximation theorem, Appl. Math. Comput. 218, (2012) 9132-9137.
  • [13] S. Ghosal, Weighted statistical convergence of order a and its applications, J. Egyptian Math. Soc. 24 no. 1 (2016) 60-67.
  • [14] K. H. Karlsen, Notes on weak convergence, University of Oslo, Norway, 2006
  • [15] I. J. Maddox, Statistical convergence in a locally convex space, Math. Proc. Cambridge Phil. Soc. 104 (1988) 141-145.
  • [16] M. İlkhan, E. E. Kara, A new type of statistical Cauchy sequence and its relation to Bourbaki completeness, Cogent Mathematics & Statistics, (2018) 5:1487500.
Year 2018, Volume: 6 Issue: 2, 194 - 199, 15.10.2018

Abstract

References

  • [1] A. Zygmund, Trigonometric Series, Cambridge University Press, New York, NY, USA, 1959.
  • [2] H. Fast, Sur la convergence statistique, Colloq. Math. 2 (1951) 241-244.
  • [3] H. Steinhaus, Sur la convergence ordinaire et la convergence asymptotique, Colloq. Math. 2 (1951) 73-74.
  • [4] A. R. Freedman, J. J. Sember, M. Raphael, Some Ces`aro-type summability spaces, Proc. Lond. Math. Soc. 37(3) (1978) 508-520.
  • [5] D. Rath, B. C. Tripathy, On statistically convergent and statistically Cauchy sequences, Indian J. Pure. Appl. Math. 25(4) (1994) 381-386. [6] T. ˇ Sal´at, On statistically convergent sequences of real numbers, Math. Slovaca 30 (1980) 139-150.
  • [7] J. Connor, M. Ganichev, V. Kadets, A characterization of Banach spaces with separable duals via weak statistical convergence, J. Math. Anal. Appl. 244 (2000) 251-261.
  • [8] V.K. Bhardwaj, I. Bala, On weak statistical convergence, Int. J. Math. Math. Sci. Art. ID 38530, (2007) 9 pp.
  • [9] Meenakshi, M. S. Saroa , V. Kumar, Weak statistical convergence defined by de la Vall´ee-Poussin mean, Bull. Calcutta Math. Soc. 106 no.3 (2014) 215-224
  • [10] V. Karakaya, T. A. Chishti, Weighted statistical convergence, Iran. J. Sci. Technol. Trans. A Sci. 33 (2009) 219-223.
  • [11] M. K¨uc¸ ¨ukaslan, Weighted statistical convergence, International Journal of Science and Technology, 2 (2012) 2-10.
  • [12] M. Mursaleen, V. Karakaya, M. Ert¨urk, F. G¨ursoy, Weighted statistical convergence and its application to Korovkin type aprroximation theorem, Appl. Math. Comput. 218, (2012) 9132-9137.
  • [13] S. Ghosal, Weighted statistical convergence of order a and its applications, J. Egyptian Math. Soc. 24 no. 1 (2016) 60-67.
  • [14] K. H. Karlsen, Notes on weak convergence, University of Oslo, Norway, 2006
  • [15] I. J. Maddox, Statistical convergence in a locally convex space, Math. Proc. Cambridge Phil. Soc. 104 (1988) 141-145.
  • [16] M. İlkhan, E. E. Kara, A new type of statistical Cauchy sequence and its relation to Bourbaki completeness, Cogent Mathematics & Statistics, (2018) 5:1487500.
There are 15 citations in total.

Details

Primary Language English
Subjects Engineering
Journal Section Articles
Authors

Sinan Ercan 0000-0001-9871-2142

Publication Date October 15, 2018
Submission Date January 5, 2018
Acceptance Date October 1, 2018
Published in Issue Year 2018 Volume: 6 Issue: 2

Cite

APA Ercan, S. (2018). On weighted weak statistical convergence. Konuralp Journal of Mathematics, 6(2), 194-199.
AMA Ercan S. On weighted weak statistical convergence. Konuralp J. Math. October 2018;6(2):194-199.
Chicago Ercan, Sinan. “On Weighted Weak Statistical Convergence”. Konuralp Journal of Mathematics 6, no. 2 (October 2018): 194-99.
EndNote Ercan S (October 1, 2018) On weighted weak statistical convergence. Konuralp Journal of Mathematics 6 2 194–199.
IEEE S. Ercan, “On weighted weak statistical convergence”, Konuralp J. Math., vol. 6, no. 2, pp. 194–199, 2018.
ISNAD Ercan, Sinan. “On Weighted Weak Statistical Convergence”. Konuralp Journal of Mathematics 6/2 (October 2018), 194-199.
JAMA Ercan S. On weighted weak statistical convergence. Konuralp J. Math. 2018;6:194–199.
MLA Ercan, Sinan. “On Weighted Weak Statistical Convergence”. Konuralp Journal of Mathematics, vol. 6, no. 2, 2018, pp. 194-9.
Vancouver Ercan S. On weighted weak statistical convergence. Konuralp J. Math. 2018;6(2):194-9.
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