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Yıl 2020, Cilt: 3 Sayı: 1, 176 - 179, 15.12.2020

Nimet Pancaroğlu Akın

Öz

Kaynakça

  • 1.B. Altay, F. Ba¸sar, Some new spaces of double sequences, J. Math. Anal. Appl. 309 (1) (2005), 70–90.
  • 2. C.Çakan, B. Altay, M. Mursaleen, The $\sigma-convergence and $\sigma-core of double sequences, Applied Mathematics Letters, 19 (2006), 1122–1128.
  • 3 P. Das, P. Kostyrko, W. Wilczy´nski, P. Malik, I and $\mathcal{I}$-convergence of double sequences, Math. Slovaca, 58(5) (2008), 605–620.
  • 4 K. Dems, On I-Cauchy sequences, Real Anal. Exchange, 30 (2004/2005), 123–128.
  • 5 E. Dündar, B. Altay, I2-convergence and I2-Cauchy of double sequences, Acta Mathematica Scientia, 34B(2) (2014), 343–353.
  • 6 E. Dündar, B. Altay, On some properties of I2-convergence and I2-Cauchy of double sequences, Gen. Math. Notes, 7 (1)(2011) 1–12.
  • 7 E. Dündar, B. Altay, I2-convergence of double sequences of functions, Electronic Journal of Mathematical Analysis and Applications, Vol. 3(1) Jan. 2015, pp. 111–121.
  • 8 E. Dündar, B. Altay I2-uniform convergence of double sequences of functions, Filomat 30(5) (2016), 1273–1281.
  • 9 E. Dündar, B. Altay, Multipliers for bounded I2-convergent of double sequences, Math. Comput. Modelling, 55(3-4) (2012), 1193–1198.
  • 10 E. Dündar. Ö. Talo, I2-convergence of double sequences of fuzzy numbers, Iranian Journal of Fuzzy Systems, 10(3) (2013), 37–50.
  • 11 E. Dündar, M. R. Türkmen and N. Pancaroˇglu Akın, Regularly ideal convergence of double sequences in fuzzy normed spaces, (in review).
  • 12 E. Dündar, Regularly (I2; I)-Convergence and (I2; I)-Cauchy Double Sequences of Functions, Pioneer Journal of Algebra, Number Theory and its Applications 1(2) (2011), 85–98.
  • 13 E. Dündar, U. Ulusu, F. Nuray, On ideal invariant convergence of double sequences and some properties, Creative Mathematics and Informatics, 27(2)(2018), 161–169.
  • 14 E. Dündar, U. Ulusu, N. Pancaroˇglu, Strongly I2-lacunary Convergence and I2-lacunary Cauchy Double Sequences of Sets, The Aligarh Bulletin of Mathematics, 35(1-2)(2016), 1–15.
  • 15 E. Dündar and N. Pancaroˇglu Akın, Wijsman Regularly Ideal Convergence of Double Sequences of Sets, Journal of Intelligent and Fuzzy Systems, (in press), DOI:10.3233/JIFS- 190626
  • 16 H. Fast, Sur la convergence statistique, Colloq. Math. 2 (1951), 241–244.
  • 17 P. Kostyrko, T. Šalát, W. Wilczy´nski, I-Convergence, Real Anal. Exchange, 26(2) (2000), 669–686.
  • 18 V. Kumar, On I and I-convergence of double sequences, Math. Commun. 12 (2007), 171–181.
  • 19 M. Mursaleen, O. H. H. Edely, Statistical convergence of double sequences, J. Math. Anal. Appl. 288 (2003) 223–231.
  • 20 M. Mursaleen, Matrix transformation between some new sequence spaces, Houston J. Math., 9 (1983), 505–509.
  • 21 M. Mursaleen, On finite matrices and invariant means, Indian J. Pure Appl. Math., 10 (1979), 457–460.
  • 22 M. Mursaleen, O. H. H. Edely, On the invariant mean and statistical convergence, Appl. Math. Lett., 22(11) (2009), 1700–1704.
  • 23 A. Nabiev, S. Pehlivan, M. Gürdal, On I-Cauchy sequence, Taiwanese J. Math. 11 (2) (2007), 569–576.
  • 24 A. Nabiev, S. Pehlivan, M. Gürdal, On I-Cauchy sequences, Taiwanese J. Math., 11(2) (2007), 569–576.
  • 25 F. Nuray, W.H. Ruckle, Generalized statistical convergence and convergence free spaces, J. Math. Anal. Appl. 245 (2000), 513–527.
  • 26 F. Nuray, H. Gök, U. Ulusu, $\mathcal{I}_{\sigma}$-convergence, Math. Commun., 16 (2011), 531–538.
  • 27 A. Pringsheim, Zur theorie der zweifach unendlichen Zahlenfolgen, Math. Ann. 53 (1900), 289–321.
  • 28 R. A. Raimi, Invariant means and invariant matrix methods of summability, Duke Math. J., 30(1) (1963), 81–94.
  • 29 E. Savş, Some sequence spaces involving invariant means, Indian J. Math., 31 (1989), 1–8.
  • 30 E. Savaş, Strongly $\sigma$-convergent sequences, Bull. Calcutta Math., 81 (1989), 295–300.
  • 31 P. Schaefer, Infinite matrices and invariant means, Proc. Amer. Math. Soc., 36 (1972), 104–110.
  • 32 I. J. Schoenberg, The integrability of certain functions and related summability methods, Amer. Math. Monthly 66 (1959) 361–375.
  • 33 Y. Sever, E. Dündar, Regularly Ideal Convergence and Regularly Ideal Cauchy Double Sequences in 2-Normed Spaces, Filomat 28:5 (2015), 907–915.
  • 34 B. Tripathy, B.C. Tripathy, On I-convergent double sequences, Soochow J. Math. 31 (2005), 549–560.
  • 35 ¸ S. Tortop, E. Dündar, Wijsman I2-invariant convergence of double sequences of sets, Journal of Inequalities and Special Functions, 9(4) (2018),90-100 .
  • 36 U. Ulusu, E. Dündar, Asymptotically lacunary I2-invariant equivalence, Journal of Intelligent and Fuzzy Systems, 36(1) (2019), 467-472, DOI:10.3233/JIFS- 181796

On Ideal Invariant Convergence of Double Sequences in Regularly Sense

Yıl 2020, Cilt: 3 Sayı: 1, 176 - 179, 15.12.2020

Nimet Pancaroğlu Akın

Öz

In this paper, we defined concepts of $r(\sigma,\sigma_2 )$-convergence, $r[\sigma,\sigma_2 ]$-convergence, $r[\sigma,\sigma_2 ]_p$-convergence, $r(\mathcal{I}_{\sigma},\mathcal{I}_{2}^{\sigma} )$-convergence of double sequences . Also we research the relationships among them. \newline\newline

Anahtar Kelimeler

double sequence invariant convergence regularly ideal convergence

Kaynakça

  • 1.B. Altay, F. Ba¸sar, Some new spaces of double sequences, J. Math. Anal. Appl. 309 (1) (2005), 70–90.
  • 2. C.Çakan, B. Altay, M. Mursaleen, The $\sigma-convergence and $\sigma-core of double sequences, Applied Mathematics Letters, 19 (2006), 1122–1128.
  • 3 P. Das, P. Kostyrko, W. Wilczy´nski, P. Malik, I and $\mathcal{I}$-convergence of double sequences, Math. Slovaca, 58(5) (2008), 605–620.
  • 4 K. Dems, On I-Cauchy sequences, Real Anal. Exchange, 30 (2004/2005), 123–128.
  • 5 E. Dündar, B. Altay, I2-convergence and I2-Cauchy of double sequences, Acta Mathematica Scientia, 34B(2) (2014), 343–353.
  • 6 E. Dündar, B. Altay, On some properties of I2-convergence and I2-Cauchy of double sequences, Gen. Math. Notes, 7 (1)(2011) 1–12.
  • 7 E. Dündar, B. Altay, I2-convergence of double sequences of functions, Electronic Journal of Mathematical Analysis and Applications, Vol. 3(1) Jan. 2015, pp. 111–121.
  • 8 E. Dündar, B. Altay I2-uniform convergence of double sequences of functions, Filomat 30(5) (2016), 1273–1281.
  • 9 E. Dündar, B. Altay, Multipliers for bounded I2-convergent of double sequences, Math. Comput. Modelling, 55(3-4) (2012), 1193–1198.
  • 10 E. Dündar. Ö. Talo, I2-convergence of double sequences of fuzzy numbers, Iranian Journal of Fuzzy Systems, 10(3) (2013), 37–50.
  • 11 E. Dündar, M. R. Türkmen and N. Pancaroˇglu Akın, Regularly ideal convergence of double sequences in fuzzy normed spaces, (in review).
  • 12 E. Dündar, Regularly (I2; I)-Convergence and (I2; I)-Cauchy Double Sequences of Functions, Pioneer Journal of Algebra, Number Theory and its Applications 1(2) (2011), 85–98.
  • 13 E. Dündar, U. Ulusu, F. Nuray, On ideal invariant convergence of double sequences and some properties, Creative Mathematics and Informatics, 27(2)(2018), 161–169.
  • 14 E. Dündar, U. Ulusu, N. Pancaroˇglu, Strongly I2-lacunary Convergence and I2-lacunary Cauchy Double Sequences of Sets, The Aligarh Bulletin of Mathematics, 35(1-2)(2016), 1–15.
  • 15 E. Dündar and N. Pancaroˇglu Akın, Wijsman Regularly Ideal Convergence of Double Sequences of Sets, Journal of Intelligent and Fuzzy Systems, (in press), DOI:10.3233/JIFS- 190626
  • 16 H. Fast, Sur la convergence statistique, Colloq. Math. 2 (1951), 241–244.
  • 17 P. Kostyrko, T. Šalát, W. Wilczy´nski, I-Convergence, Real Anal. Exchange, 26(2) (2000), 669–686.
  • 18 V. Kumar, On I and I-convergence of double sequences, Math. Commun. 12 (2007), 171–181.
  • 19 M. Mursaleen, O. H. H. Edely, Statistical convergence of double sequences, J. Math. Anal. Appl. 288 (2003) 223–231.
  • 20 M. Mursaleen, Matrix transformation between some new sequence spaces, Houston J. Math., 9 (1983), 505–509.
  • 21 M. Mursaleen, On finite matrices and invariant means, Indian J. Pure Appl. Math., 10 (1979), 457–460.
  • 22 M. Mursaleen, O. H. H. Edely, On the invariant mean and statistical convergence, Appl. Math. Lett., 22(11) (2009), 1700–1704.
  • 23 A. Nabiev, S. Pehlivan, M. Gürdal, On I-Cauchy sequence, Taiwanese J. Math. 11 (2) (2007), 569–576.
  • 24 A. Nabiev, S. Pehlivan, M. Gürdal, On I-Cauchy sequences, Taiwanese J. Math., 11(2) (2007), 569–576.
  • 25 F. Nuray, W.H. Ruckle, Generalized statistical convergence and convergence free spaces, J. Math. Anal. Appl. 245 (2000), 513–527.
  • 26 F. Nuray, H. Gök, U. Ulusu, $\mathcal{I}_{\sigma}$-convergence, Math. Commun., 16 (2011), 531–538.
  • 27 A. Pringsheim, Zur theorie der zweifach unendlichen Zahlenfolgen, Math. Ann. 53 (1900), 289–321.
  • 28 R. A. Raimi, Invariant means and invariant matrix methods of summability, Duke Math. J., 30(1) (1963), 81–94.
  • 29 E. Savş, Some sequence spaces involving invariant means, Indian J. Math., 31 (1989), 1–8.
  • 30 E. Savaş, Strongly $\sigma$-convergent sequences, Bull. Calcutta Math., 81 (1989), 295–300.
  • 31 P. Schaefer, Infinite matrices and invariant means, Proc. Amer. Math. Soc., 36 (1972), 104–110.
  • 32 I. J. Schoenberg, The integrability of certain functions and related summability methods, Amer. Math. Monthly 66 (1959) 361–375.
  • 33 Y. Sever, E. Dündar, Regularly Ideal Convergence and Regularly Ideal Cauchy Double Sequences in 2-Normed Spaces, Filomat 28:5 (2015), 907–915.
  • 34 B. Tripathy, B.C. Tripathy, On I-convergent double sequences, Soochow J. Math. 31 (2005), 549–560.
  • 35 ¸ S. Tortop, E. Dündar, Wijsman I2-invariant convergence of double sequences of sets, Journal of Inequalities and Special Functions, 9(4) (2018),90-100 .
  • 36 U. Ulusu, E. Dündar, Asymptotically lacunary I2-invariant equivalence, Journal of Intelligent and Fuzzy Systems, 36(1) (2019), 467-472, DOI:10.3233/JIFS- 181796
Toplam 36 adet kaynakça vardır.

Ayrıntılar

Birincil Dil İngilizce
Konular Mühendislik
Bölüm Articles
Yazarlar

Nimet Pancaroğlu Akın

Yayımlanma Tarihi 15 Aralık 2020
Kabul Tarihi 27 Eylül 2020
Yayımlandığı Sayı Yıl 2020 Cilt: 3 Sayı: 1

Kaynak Göster

APA Pancaroğlu Akın, N. (2020). On Ideal Invariant Convergence of Double Sequences in Regularly Sense. Conference Proceedings of Science and Technology, 3(1), 176-179.
AMA Pancaroğlu Akın N. On Ideal Invariant Convergence of Double Sequences in Regularly Sense. Conference Proceedings of Science and Technology. Aralık 2020;3(1):176-179.
Chicago Pancaroğlu Akın, Nimet. “On Ideal Invariant Convergence of Double Sequences in Regularly Sense”. Conference Proceedings of Science and Technology 3, sy. 1 (Aralık 2020): 176-79.
EndNote Pancaroğlu Akın N (01 Aralık 2020) On Ideal Invariant Convergence of Double Sequences in Regularly Sense. Conference Proceedings of Science and Technology 3 1 176–179.
IEEE N. Pancaroğlu Akın, “On Ideal Invariant Convergence of Double Sequences in Regularly Sense”, Conference Proceedings of Science and Technology, c. 3, sy. 1, ss. 176–179, 2020.
ISNAD Pancaroğlu Akın, Nimet. “On Ideal Invariant Convergence of Double Sequences in Regularly Sense”. Conference Proceedings of Science and Technology 3/1 (Aralık 2020), 176-179.
JAMA Pancaroğlu Akın N. On Ideal Invariant Convergence of Double Sequences in Regularly Sense. Conference Proceedings of Science and Technology. 2020;3:176–179.
MLA Pancaroğlu Akın, Nimet. “On Ideal Invariant Convergence of Double Sequences in Regularly Sense”. Conference Proceedings of Science and Technology, c. 3, sy. 1, 2020, ss. 176-9.
Vancouver Pancaroğlu Akın N. On Ideal Invariant Convergence of Double Sequences in Regularly Sense. Conference Proceedings of Science and Technology. 2020;3(1):176-9.
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