Research Article

$f$-Asymptotically $\mathcal{I}_{\sigma\theta}$-Equivalence of Real Sequences

Volume: 3 Number: 1 April 24, 2020
EN

$f$-Asymptotically $\mathcal{I}_{\sigma\theta}$-Equivalence of Real Sequences

Abstract

In this manuscript, we present the ideas of asymptotically $[{\mathcal{I}_{\sigma\theta}}]$-equivalence, asymptotically ${\mathcal{I}_{\sigma\theta}}(f)$-equivalence, asymptotically $[{\mathcal{I}_{\sigma\theta}}(f)]$-equivalence and asymptotically ${\mathcal{I}(S_{\sigma\theta})}$-equivalence for real sequences. In addition to, investigate some connections among these new ideas and we give some inclusion theorems about them.

Keywords

Asymptotically equivalence,Lacunary invariant equivalence,$\mathcal{I}$-equivalence,Modulus function

References

  1. [1] H. Fast, Sur la convergence statistique, Colloq. Math. 2 (1951), 241–244.
  2. [2] I. J. Schoenberg, The integrability of certain functions and related summability methods, Amer. Math. Monthly, 66 (1959), 361–375.
  3. [3] P. Kostyrko, T. Salat, W. Wilczy´nski, I-Convergence, Real Anal. Exchange, 26(2) (2000), 669–686.
  4. [4] R. A. Raimi, Invariant means and invariant matrix methods of summability, Duke Math. J., 30 (1963), 81–94.
  5. [5] P. Schaefer, Infinite matrices and invariant means, Proc. Amer. Math. Soc., 36 (1972), 104–110.
  6. [6] M. Mursaleen, O. H. H. Edely, On the invariant mean and statistical convergence, Appl. Math. Lett., 22 (2009), 1700–1704.
  7. [7] M. Mursaleen, On finite matrices and invariant means, Indian J. Pure and Appl. Math., 10 (1979), 457–460.
  8. [8] E. Savas, Some sequence spaces involving invariant means, Indian J. Math., 31 (1989), 1–8.
  9. [9] E. Savas, Strong s-convergent sequences, Bull. Calcutta Math., 81 (1989), 295–300.
  10. [10] E. Savas, On lacunary strong s-convergence, Indian J. Pure Appl. Math., 21(4) (1990), 359–365.
APA
Dundar, E., & Akın, N. (2020). $f$-Asymptotically $\mathcal{I}_{\sigma\theta}$-Equivalence of Real Sequences. Journal of Mathematical Sciences and Modelling, 3(1), 32-37. https://doi.org/10.33187/jmsm.710084
AMA
1.Dundar E, Akın N. $f$-Asymptotically $\mathcal{I}_{\sigma\theta}$-Equivalence of Real Sequences. Journal of Mathematical Sciences and Modelling. 2020;3(1):32-37. doi:10.33187/jmsm.710084
Chicago
Dundar, Erdinç, and Nimet Akın. 2020. “$f$-Asymptotically $\mathcal{I}_{\sigma\theta}$-Equivalence of Real Sequences”. Journal of Mathematical Sciences and Modelling 3 (1): 32-37. https://doi.org/10.33187/jmsm.710084.
EndNote
Dundar E, Akın N (April 1, 2020) $f$-Asymptotically $\mathcal{I}_{\sigma\theta}$-Equivalence of Real Sequences. Journal of Mathematical Sciences and Modelling 3 1 32–37.
IEEE
[1]E. Dundar and N. Akın, “$f$-Asymptotically $\mathcal{I}_{\sigma\theta}$-Equivalence of Real Sequences”, Journal of Mathematical Sciences and Modelling, vol. 3, no. 1, pp. 32–37, Apr. 2020, doi: 10.33187/jmsm.710084.
ISNAD
Dundar, Erdinç - Akın, Nimet. “$f$-Asymptotically $\mathcal{I}_{\sigma\theta}$-Equivalence of Real Sequences”. Journal of Mathematical Sciences and Modelling 3/1 (April 1, 2020): 32-37. https://doi.org/10.33187/jmsm.710084.
JAMA
1.Dundar E, Akın N. $f$-Asymptotically $\mathcal{I}_{\sigma\theta}$-Equivalence of Real Sequences. Journal of Mathematical Sciences and Modelling. 2020;3:32–37.
MLA
Dundar, Erdinç, and Nimet Akın. “$f$-Asymptotically $\mathcal{I}_{\sigma\theta}$-Equivalence of Real Sequences”. Journal of Mathematical Sciences and Modelling, vol. 3, no. 1, Apr. 2020, pp. 32-37, doi:10.33187/jmsm.710084.
Vancouver
1.Erdinç Dundar, Nimet Akın. $f$-Asymptotically $\mathcal{I}_{\sigma\theta}$-Equivalence of Real Sequences. Journal of Mathematical Sciences and Modelling. 2020 Apr. 1;3(1):32-7. doi:10.33187/jmsm.710084