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

Erdinç Dundar; Nimet Akın

doi:10.33187/jmsm.710084

Araştırma Makalesi

Yıl 2020, Cilt: 3 Sayı: 1, 32 - 37, 24.04.2020

Erdinç Dundar Nimet Akın

https://doi.org/10.33187/jmsm.710084

Öz

Kaynakça

[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

Yıl 2020, Cilt: 3 Sayı: 1, 32 - 37, 24.04.2020

Erdinç Dundar Nimet Akın

https://doi.org/10.33187/jmsm.710084

Öz

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.

Anahtar Kelimeler

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

Kaynakça

[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.

Toplam 26 adet kaynakça vardır.

Ayrıntılar

Birincil Dil	İngilizce
Konular	Matematik
Bölüm	Makaleler
Yazarlar	Erdinç Dundar Nimet Akın
Yayımlanma Tarihi	24 Nisan 2020
Gönderilme Tarihi	27 Mart 2020
Kabul Tarihi	15 Nisan 2020
Yayımlandığı Sayı	Yıl 2020 Cilt: 3 Sayı: 1

Kaynak Göster

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. Nisan 2020;3(1):32-37. doi:10.33187/jmsm.710084
Chicago	Dundar, Erdinç, ve Nimet Akın. “$f$-Asymptotically $\mathcal{I}_{\sigma\theta}$-Equivalence of Real Sequences”. Journal of Mathematical Sciences and Modelling 3, sy. 1 (Nisan 2020): 32-37. https://doi.org/10.33187/jmsm.710084.
EndNote	Dundar E, Akın N (01 Nisan 2020) $f$-Asymptotically $\mathcal{I}_{\sigma\theta}$-Equivalence of Real Sequences. Journal of Mathematical Sciences and Modelling 3 1 32–37.
IEEE	E. Dundar ve N. Akın, “$f$-Asymptotically $\mathcal{I}_{\sigma\theta}$-Equivalence of Real Sequences”, Journal of Mathematical Sciences and Modelling, c. 3, sy. 1, ss. 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 (Nisan 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 ve Nimet Akın. “$f$-Asymptotically $\mathcal{I}_{\sigma\theta}$-Equivalence of Real Sequences”. Journal of Mathematical Sciences and Modelling, c. 3, sy. 1, 2020, ss. 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.