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Year 2020, , 32 - 37, 24.04.2020
https://doi.org/10.33187/jmsm.710084

Abstract

References

  • [1] H. Fast, Sur la convergence statistique, Colloq. Math. 2 (1951), 241–244.
  • [2] I. J. Schoenberg, The integrability of certain functions and related summability methods, Amer. Math. Monthly, 66 (1959), 361–375.
  • [3] P. Kostyrko, T. Salat, W. Wilczy´nski, I-Convergence, Real Anal. Exchange, 26(2) (2000), 669–686.
  • [4] R. A. Raimi, Invariant means and invariant matrix methods of summability, Duke Math. J., 30 (1963), 81–94.
  • [5] P. Schaefer, Infinite matrices and invariant means, Proc. Amer. Math. Soc., 36 (1972), 104–110.
  • [6] M. Mursaleen, O. H. H. Edely, On the invariant mean and statistical convergence, Appl. Math. Lett., 22 (2009), 1700–1704.
  • [7] M. Mursaleen, On finite matrices and invariant means, Indian J. Pure and Appl. Math., 10 (1979), 457–460.
  • [8] E. Savas, Some sequence spaces involving invariant means, Indian J. Math., 31 (1989), 1–8.
  • [9] E. Savas, Strong s-convergent sequences, Bull. Calcutta Math., 81 (1989), 295–300.
  • [10] E. Savas, On lacunary strong s-convergence, Indian J. Pure Appl. Math., 21(4) (1990), 359–365.
  • [11] F. Nuray, E. Savas, Invariant statistical convergence and A-invariant statistical convergence, Indian J. Pure Appl. Math., 10 (1994), 267–274.
  • [12] N. Pancaroglu, F. Nuray, Statistical lacunary invariant summability, Theor. Math. Appl., 3(2) (2013), 71–78.
  • [13] E. Savas, F. Nuray, On s-statistically convergence and lacunary s-statistically convergence, Math. Slovaca, 43(3) (1993), 309–315.
  • [14] F. Nuray, H. G¨ok, U. Ulusu, Is -convergence, Math. Commun., 16 (2011), 531–538.
  • [15] U. Ulusu, F. Nuray, Lacunary Is -convergence, (submitted).
  • [16] M. Marouf, Asymptotic equivalence and summability, Int. J. Math. Math. Sci., 16(4) (1993), 755-762.
  • [17] R. F. Patterson, E. Savas, On asymptotically lacunary statistically equivalent sequences, Thai J. Math., 4(2) (2006), 267–272.
  • [18] E. Savas, R. F. Patterson, s-asymptotically lacunary statistical equivalent sequences, Cent. Eur. J. Math., 4(4) (2006), 648-655.
  • [19] U. Ulusu, Asymptotoically lacunary Is -equivalence, Afyon Kocatepe University Journal of Science and Engineering, 17 (2017), 899-905.
  • [20] U. Ulusu, Asymptotoically ideal invariant equivalence, Creat. Math. Inform., 27 (2018), 215-220.
  • [21] H. Nakano, Concave modulars, J. Math. Soc. Japan, 5 (1953), 29-49.
  • [22] I. J. Maddox, Sequence spaces defined by a modulus, Math. Proc. Camb. Phil. Soc. 100 (1986), 161–166.
  • [23] S. Pehlivan, B. Fisher, Some sequences spaces defined by a modulus, Math. Slovaca, 45 (1995), 275-280.
  • [24] V. Kumar, A. Sharma, Asymptotically lacunary equivalent sequences defined by ideals and modulus function, Math. Sci., 6(23) (2012), 5 pages.
  • [25] E. Dundar and N. Pancaroğlu Akın, f -Asymptotically Is -Equivalence of Real Sequences, Konuralp J. Math., (in press).
  • [26] M. Mursaleen, Matrix transformation between some new sequence spaces, Houston J. Math., 9 (1983), 505–509.

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

Year 2020, , 32 - 37, 24.04.2020
https://doi.org/10.33187/jmsm.710084

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.

References

  • [1] H. Fast, Sur la convergence statistique, Colloq. Math. 2 (1951), 241–244.
  • [2] I. J. Schoenberg, The integrability of certain functions and related summability methods, Amer. Math. Monthly, 66 (1959), 361–375.
  • [3] P. Kostyrko, T. Salat, W. Wilczy´nski, I-Convergence, Real Anal. Exchange, 26(2) (2000), 669–686.
  • [4] R. A. Raimi, Invariant means and invariant matrix methods of summability, Duke Math. J., 30 (1963), 81–94.
  • [5] P. Schaefer, Infinite matrices and invariant means, Proc. Amer. Math. Soc., 36 (1972), 104–110.
  • [6] M. Mursaleen, O. H. H. Edely, On the invariant mean and statistical convergence, Appl. Math. Lett., 22 (2009), 1700–1704.
  • [7] M. Mursaleen, On finite matrices and invariant means, Indian J. Pure and Appl. Math., 10 (1979), 457–460.
  • [8] E. Savas, Some sequence spaces involving invariant means, Indian J. Math., 31 (1989), 1–8.
  • [9] E. Savas, Strong s-convergent sequences, Bull. Calcutta Math., 81 (1989), 295–300.
  • [10] E. Savas, On lacunary strong s-convergence, Indian J. Pure Appl. Math., 21(4) (1990), 359–365.
  • [11] F. Nuray, E. Savas, Invariant statistical convergence and A-invariant statistical convergence, Indian J. Pure Appl. Math., 10 (1994), 267–274.
  • [12] N. Pancaroglu, F. Nuray, Statistical lacunary invariant summability, Theor. Math. Appl., 3(2) (2013), 71–78.
  • [13] E. Savas, F. Nuray, On s-statistically convergence and lacunary s-statistically convergence, Math. Slovaca, 43(3) (1993), 309–315.
  • [14] F. Nuray, H. G¨ok, U. Ulusu, Is -convergence, Math. Commun., 16 (2011), 531–538.
  • [15] U. Ulusu, F. Nuray, Lacunary Is -convergence, (submitted).
  • [16] M. Marouf, Asymptotic equivalence and summability, Int. J. Math. Math. Sci., 16(4) (1993), 755-762.
  • [17] R. F. Patterson, E. Savas, On asymptotically lacunary statistically equivalent sequences, Thai J. Math., 4(2) (2006), 267–272.
  • [18] E. Savas, R. F. Patterson, s-asymptotically lacunary statistical equivalent sequences, Cent. Eur. J. Math., 4(4) (2006), 648-655.
  • [19] U. Ulusu, Asymptotoically lacunary Is -equivalence, Afyon Kocatepe University Journal of Science and Engineering, 17 (2017), 899-905.
  • [20] U. Ulusu, Asymptotoically ideal invariant equivalence, Creat. Math. Inform., 27 (2018), 215-220.
  • [21] H. Nakano, Concave modulars, J. Math. Soc. Japan, 5 (1953), 29-49.
  • [22] I. J. Maddox, Sequence spaces defined by a modulus, Math. Proc. Camb. Phil. Soc. 100 (1986), 161–166.
  • [23] S. Pehlivan, B. Fisher, Some sequences spaces defined by a modulus, Math. Slovaca, 45 (1995), 275-280.
  • [24] V. Kumar, A. Sharma, Asymptotically lacunary equivalent sequences defined by ideals and modulus function, Math. Sci., 6(23) (2012), 5 pages.
  • [25] E. Dundar and N. Pancaroğlu Akın, f -Asymptotically Is -Equivalence of Real Sequences, Konuralp J. Math., (in press).
  • [26] M. Mursaleen, Matrix transformation between some new sequence spaces, Houston J. Math., 9 (1983), 505–509.
There are 26 citations in total.

Details

Primary Language English
Subjects Mathematical Sciences
Journal Section Articles
Authors

Erdinç Dundar

Nimet Akın

Publication Date April 24, 2020
Submission Date March 27, 2020
Acceptance Date April 15, 2020
Published in Issue Year 2020

Cite

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 Dundar E, Akın N. $f$-Asymptotically $\mathcal{I}_{\sigma\theta}$-Equivalence of Real Sequences. Journal of Mathematical Sciences and Modelling. April 2020;3(1):32-37. doi:10.33187/jmsm.710084
Chicago Dundar, Erdinç, and Nimet Akın. “$f$-Asymptotically $\mathcal{I}_{\sigma\theta}$-Equivalence of Real Sequences”. Journal of Mathematical Sciences and Modelling 3, no. 1 (April 2020): 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 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, 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 2020), 32-37. https://doi.org/10.33187/jmsm.710084.
JAMA 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, 2020, pp. 32-37, doi:10.33187/jmsm.710084.
Vancouver Dundar E, Akın N. $f$-Asymptotically $\mathcal{I}_{\sigma\theta}$-Equivalence of Real Sequences. Journal of Mathematical Sciences and Modelling. 2020;3(1):32-7.

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