Araştırma Makalesi
BibTex RIS Kaynak Göster
Yıl 2020, Cilt: 8 Sayı: 1, 207 - 210, 15.04.2020

Öz

Kaynakça

  • [1] J.S. Connor, On strong matrix summability with respect to a modulus and statistical convergence, Canad. Math. Bull. 32 (1989), 194-198.
  • [2] H. Fast, Sur la convergence statistique, Colloq. Math. 2 (1951), 241–244.
  • [3] E. Kolk, On strong boundedness and summability with respect to a sequence of moduli, TartuUl. Toimetised, 960 (1993), 41-50.
  • [4] P. Kostyrko, T. Salat, W. Wilczynski, I-Convergence, Real Anal. Exchange, 26(2) (2000), 669–686.
  • [5] V. Kumar, A. Sharma, Asymptotically lacunary equivalent sequences defined by ideals and modulus function, Mathematical Sciences, 6(23) (2012), 5 pages.
  • [6] G. Lorentz, A contribution to the theory of divergent sequences, Acta Math. 80 (1948), 167–190.
  • [7] I. J. Maddox, Sequence spaces defined by a modulus, Math. Proc. Camb. Phil. Soc. 100 (1986), 161–166.
  • [8] M. Marouf, Asymptotic equivalence and summability, Int. J. Math. Math. Sci. 16(4) (1993), 755-762.
  • [9] M. Mursaleen, O. H. H. Edely, On the invariant mean and statistical convergence, Appl. Math. Lett. 22 (2009), 1700–1704.
  • [10] M. Mursaleen, Matrix transformation between some new sequence spaces, Houston J. Math. 9 (1983), 505–509.
  • [11] M. Mursaleen, On finite matrices and invariant means, Indian J. Pure and Appl. Math. 10 (1979), 457–460.
  • [12] H. Nakano, Concave modulars, J. Math. Soc. Japan, 5 (1953), 29-49.
  • [13] F. Nuray, E. Savas¸, Invariant statistical convergence and A-invariant statistical convergence, Indian J. Pure Appl. Math. 10 (1994), 267–274.
  • [14] F. Nuray, H. G¨ok, U. Ulusu, Is -convergence, Math. Commun. 16 (2011), 531–538.
  • [15] N. Pancaroˇglu, F. Nuray, Statistical lacunary invariant summability, Theoretical Mathematics and Applications, 3(2) (2013), 71–78.
  • [16] R. F. Patterson, On asymptotically statistically equivalent sequences, Demostratio Mathematica, 36(1) (2003), 149–153.
  • [17] S. Pehlivan, B. Fisher, Some sequences spaces defined by a modulus, Mathematica Slovaca, 45 (1995), 275-280.
  • [18] R. A. Raimi, Invariant means and invariant matrix methods of summability, Duke Math. J. 30 (1963), 81–94.
  • [19] E. Savas¸, Some sequence spaces involving invariant means, Indian J. Math. 31 (1989), 1–8.
  • [20] E. Savas¸, Strong s-convergent sequences, Bull. Calcutta Math. 81 (1989), 295–300.
  • [21] E. Savas¸, F. Nuray, On s-statistically convergence and lacunary s-statistically convergence, Math. Slovaca, 43(3) (1993), 309–315.
  • [22] P. Schaefer, Infinite matrices and invariant means, Proc. Amer. Math. Soc. 36 (1972), 104–110.
  • [23] I. J. Schoenberg, The integrability of certain functions and related summability methods, Amer. Math. Monthly, 66 (1959), 361–375.
  • [24] U. Ulusu, Asymptotoically ideal invariant equivalence, Creat. Math. Inform. 27 (2018), 215-220.

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

Yıl 2020, Cilt: 8 Sayı: 1, 207 - 210, 15.04.2020

Öz

In this study, we present the notions of strongly asymptotically $\mathcal{I}$-invariant equivalence, $f$-asymptotically $\mathcal{I}$-invariant equivalence, strongly $f$-asymptotically $\mathcal{I}$-invariant equivalence and asymptotically $\mathcal{I}$-invariant statistical equivalence for real sequences. Also, we investigate some relationships among them.

Kaynakça

  • [1] J.S. Connor, On strong matrix summability with respect to a modulus and statistical convergence, Canad. Math. Bull. 32 (1989), 194-198.
  • [2] H. Fast, Sur la convergence statistique, Colloq. Math. 2 (1951), 241–244.
  • [3] E. Kolk, On strong boundedness and summability with respect to a sequence of moduli, TartuUl. Toimetised, 960 (1993), 41-50.
  • [4] P. Kostyrko, T. Salat, W. Wilczynski, I-Convergence, Real Anal. Exchange, 26(2) (2000), 669–686.
  • [5] V. Kumar, A. Sharma, Asymptotically lacunary equivalent sequences defined by ideals and modulus function, Mathematical Sciences, 6(23) (2012), 5 pages.
  • [6] G. Lorentz, A contribution to the theory of divergent sequences, Acta Math. 80 (1948), 167–190.
  • [7] I. J. Maddox, Sequence spaces defined by a modulus, Math. Proc. Camb. Phil. Soc. 100 (1986), 161–166.
  • [8] M. Marouf, Asymptotic equivalence and summability, Int. J. Math. Math. Sci. 16(4) (1993), 755-762.
  • [9] M. Mursaleen, O. H. H. Edely, On the invariant mean and statistical convergence, Appl. Math. Lett. 22 (2009), 1700–1704.
  • [10] M. Mursaleen, Matrix transformation between some new sequence spaces, Houston J. Math. 9 (1983), 505–509.
  • [11] M. Mursaleen, On finite matrices and invariant means, Indian J. Pure and Appl. Math. 10 (1979), 457–460.
  • [12] H. Nakano, Concave modulars, J. Math. Soc. Japan, 5 (1953), 29-49.
  • [13] F. Nuray, E. Savas¸, Invariant statistical convergence and A-invariant statistical convergence, Indian J. Pure Appl. Math. 10 (1994), 267–274.
  • [14] F. Nuray, H. G¨ok, U. Ulusu, Is -convergence, Math. Commun. 16 (2011), 531–538.
  • [15] N. Pancaroˇglu, F. Nuray, Statistical lacunary invariant summability, Theoretical Mathematics and Applications, 3(2) (2013), 71–78.
  • [16] R. F. Patterson, On asymptotically statistically equivalent sequences, Demostratio Mathematica, 36(1) (2003), 149–153.
  • [17] S. Pehlivan, B. Fisher, Some sequences spaces defined by a modulus, Mathematica Slovaca, 45 (1995), 275-280.
  • [18] R. A. Raimi, Invariant means and invariant matrix methods of summability, Duke Math. J. 30 (1963), 81–94.
  • [19] E. Savas¸, Some sequence spaces involving invariant means, Indian J. Math. 31 (1989), 1–8.
  • [20] E. Savas¸, Strong s-convergent sequences, Bull. Calcutta Math. 81 (1989), 295–300.
  • [21] E. Savas¸, F. Nuray, On s-statistically convergence and lacunary s-statistically convergence, Math. Slovaca, 43(3) (1993), 309–315.
  • [22] P. Schaefer, Infinite matrices and invariant means, Proc. Amer. Math. Soc. 36 (1972), 104–110.
  • [23] I. J. Schoenberg, The integrability of certain functions and related summability methods, Amer. Math. Monthly, 66 (1959), 361–375.
  • [24] U. Ulusu, Asymptotoically ideal invariant equivalence, Creat. Math. Inform. 27 (2018), 215-220.
Toplam 24 adet kaynakça vardır.

Ayrıntılar

Birincil Dil İngilizce
Konular Mühendislik
Bölüm Articles
Yazarlar

Erdinç Dundar

Nimet Akın

Yayımlanma Tarihi 15 Nisan 2020
Gönderilme Tarihi 26 Mart 2020
Kabul Tarihi 11 Nisan 2020
Yayımlandığı Sayı Yıl 2020 Cilt: 8 Sayı: 1

Kaynak Göster

APA Dundar, E., & Akın, N. (2020). $f$-Asymptotically $\mathcal{I}_{\sigma}$-Equivalence of Real Sequences. Konuralp Journal of Mathematics, 8(1), 207-210.
AMA Dundar E, Akın N. $f$-Asymptotically $\mathcal{I}_{\sigma}$-Equivalence of Real Sequences. Konuralp J. Math. Nisan 2020;8(1):207-210.
Chicago Dundar, Erdinç, ve Nimet Akın. “$f$-Asymptotically $\mathcal{I}_{\sigma}$-Equivalence of Real Sequences”. Konuralp Journal of Mathematics 8, sy. 1 (Nisan 2020): 207-10.
EndNote Dundar E, Akın N (01 Nisan 2020) $f$-Asymptotically $\mathcal{I}_{\sigma}$-Equivalence of Real Sequences. Konuralp Journal of Mathematics 8 1 207–210.
IEEE E. Dundar ve N. Akın, “$f$-Asymptotically $\mathcal{I}_{\sigma}$-Equivalence of Real Sequences”, Konuralp J. Math., c. 8, sy. 1, ss. 207–210, 2020.
ISNAD Dundar, Erdinç - Akın, Nimet. “$f$-Asymptotically $\mathcal{I}_{\sigma}$-Equivalence of Real Sequences”. Konuralp Journal of Mathematics 8/1 (Nisan 2020), 207-210.
JAMA Dundar E, Akın N. $f$-Asymptotically $\mathcal{I}_{\sigma}$-Equivalence of Real Sequences. Konuralp J. Math. 2020;8:207–210.
MLA Dundar, Erdinç ve Nimet Akın. “$f$-Asymptotically $\mathcal{I}_{\sigma}$-Equivalence of Real Sequences”. Konuralp Journal of Mathematics, c. 8, sy. 1, 2020, ss. 207-10.
Vancouver Dundar E, Akın N. $f$-Asymptotically $\mathcal{I}_{\sigma}$-Equivalence of Real Sequences. Konuralp J. Math. 2020;8(1):207-10.
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