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On subsequentially convergent sequences

Year 2019, Volume: 68 Issue: 2, 1473 - 1481, 01.08.2019

S.a. Sezer İ. Çanak

https://doi.org/10.31801/cfsuasmas.540620

Abstract

In this study we obtain some sufficient conditions under which subsequential convergence of a sequence of real numbers follows from its boundedness. Eventually, we obtain crucial information about the subsequential behavior of sequences.

Keywords

Subsequential convergence slowly oscillating sequences logarithmic summability

References

  • Çanak, İ. and Totur, Ü., Some conditions for subsequential convergence and ordinary convergence, J. Comput. Anal. Appl. 14(3) (2012), 466-474.
  • Çanak, İ. and Totur, Ü., On subsequential convergence of bounded sequences, Miskolc Math. Notes. 16(2) (2015), 721-728.
  • Dik, F., Tauberian theorems for convergence and subsequential convergence with moderately oscillatory behavior, Math. Morav. 5 (2001), 19-56.
  • Dik, F., Dik, M. and Çanak, İ., Applications of subsequential Tauberian theory to classical Tauberian theory, Appl. Math. Lett. 20(8) (2007), 946-950.
  • Ishiguro, K., Tauberian theorems concerning the summability methods of logarithmic type, Proc. Japan Acad. 39 (1963), 156-159.
  • Kwee, B., A Tauberian theorem for the logarithmic method of summation, Proc. Cambridge Philos. Soc. 63 (1967), 401-405.
  • Kwee, B., Some Tauberian theorems for the logarithmic method of summability, Canad. J. Math. 20 (1968), 1324-1331.
  • Sezer, S. A. and Çanak, İ., Convergence and subsequential convergence of regularly generated sequences, Miskolc Math. Notes. 16(2) (2015), 1181-1189.
  • Sezer, S. A. and Çanak, İ., Tauberian theorems for the summability methods of logarithmic type, Bull. Malays. Math. Sci. Soc. 41(4) (2018), 1977-1994.
  • Stanojević, Č.V., Analysis of Divergence: Applications to the Tauberian theory in: Graduate Research Seminar, University of Missouri-Rolla, 1999.

Year 2019, Volume: 68 Issue: 2, 1473 - 1481, 01.08.2019

S.a. Sezer İ. Çanak

https://doi.org/10.31801/cfsuasmas.540620

Abstract

References

  • Çanak, İ. and Totur, Ü., Some conditions for subsequential convergence and ordinary convergence, J. Comput. Anal. Appl. 14(3) (2012), 466-474.
  • Çanak, İ. and Totur, Ü., On subsequential convergence of bounded sequences, Miskolc Math. Notes. 16(2) (2015), 721-728.
  • Dik, F., Tauberian theorems for convergence and subsequential convergence with moderately oscillatory behavior, Math. Morav. 5 (2001), 19-56.
  • Dik, F., Dik, M. and Çanak, İ., Applications of subsequential Tauberian theory to classical Tauberian theory, Appl. Math. Lett. 20(8) (2007), 946-950.
  • Ishiguro, K., Tauberian theorems concerning the summability methods of logarithmic type, Proc. Japan Acad. 39 (1963), 156-159.
  • Kwee, B., A Tauberian theorem for the logarithmic method of summation, Proc. Cambridge Philos. Soc. 63 (1967), 401-405.
  • Kwee, B., Some Tauberian theorems for the logarithmic method of summability, Canad. J. Math. 20 (1968), 1324-1331.
  • Sezer, S. A. and Çanak, İ., Convergence and subsequential convergence of regularly generated sequences, Miskolc Math. Notes. 16(2) (2015), 1181-1189.
  • Sezer, S. A. and Çanak, İ., Tauberian theorems for the summability methods of logarithmic type, Bull. Malays. Math. Sci. Soc. 41(4) (2018), 1977-1994.
  • Stanojević, Č.V., Analysis of Divergence: Applications to the Tauberian theory in: Graduate Research Seminar, University of Missouri-Rolla, 1999.
There are 10 citations in total.

Details

Primary Language English
Subjects Mathematical Sciences
Journal Section Review Articles
Authors

S.a. Sezer 0000-0002-8053-9991

İ. Çanak 0000-0002-1754-1685

Publication Date August 1, 2019
Submission Date July 31, 2018
Acceptance Date January 15, 2019
Published in Issue Year 2019 Volume: 68 Issue: 2

Cite

APA Sezer, S., & Çanak, İ. (2019). On subsequentially convergent sequences. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics, 68(2), 1473-1481. https://doi.org/10.31801/cfsuasmas.540620
AMA Sezer S, Çanak İ. On subsequentially convergent sequences. Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat. August 2019;68(2):1473-1481. doi:10.31801/cfsuasmas.540620
Chicago Sezer, S.a., and İ. Çanak. “On Subsequentially Convergent Sequences”. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics 68, no. 2 (August 2019): 1473-81. https://doi.org/10.31801/cfsuasmas.540620.
EndNote Sezer S, Çanak İ (August 1, 2019) On subsequentially convergent sequences. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics 68 2 1473–1481.
IEEE S. Sezer and İ. Çanak, “On subsequentially convergent sequences”, Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat., vol. 68, no. 2, pp. 1473–1481, 2019, doi: 10.31801/cfsuasmas.540620.
ISNAD Sezer, S.a. - Çanak, İ. “On Subsequentially Convergent Sequences”. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics 68/2 (August 2019), 1473-1481. https://doi.org/10.31801/cfsuasmas.540620.
JAMA Sezer S, Çanak İ. On subsequentially convergent sequences. Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat. 2019;68:1473–1481.
MLA Sezer, S.a. and İ. Çanak. “On Subsequentially Convergent Sequences”. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics, vol. 68, no. 2, 2019, pp. 1473-81, doi:10.31801/cfsuasmas.540620.
Vancouver Sezer S, Çanak İ. On subsequentially convergent sequences. Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat. 2019;68(2):1473-81.

Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics.

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