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$\mathcal{I}_2$-Convergence of Double Sequences of Functions in 2-Normed Spaces

Yıl 2019, Cilt: 2 Sayı: 3, 130 - 137, 30.09.2019

Sevim Yegül Erdinç Dündar

https://doi.org/10.32323/ujma.606050
Cited By: 1

Öz

In this study, we introduced the concepts of $\mathcal{I}_2$-convergence and $\mathcal{I}_2^*$-convergence of double sequences of functions in $2$-normed space. Also, were studied some properties about these concepts and investigated relationships between them for double sequences of functions in $2$-normed spaces.

Anahtar Kelimeler

Double sequences of functions 2-normed Spaces $\mathcal{I}_2$-convergence $\mathcal{I}_2^*$-convergence

Kaynakça

  • [1] M. Arslan, E. Dündar, I-Convergence and I-Cauchy Sequence of Functions In 2-Normed Spaces, Konuralp J. Math., 6(1) (2018), 57–62.
  • [2] M. Arslan, E. Dündar, On I-Convergence of sequences of functions in 2-normed spaces, Southeast Asian Bull. Math., 42 (2018), 491–502.
  • [3] M. Arslan, E. Dündar, Rough convergence in 2-normed spaces, Bull. Math. Anal. Appl., 10(3) (2018), 1–9.
  • [4] V. Balaz, J. Cervenansky, P. Kostyrko, T. Salat, I-convergence and I-continuity of real functions, Acta Math., Faculty of Natural Sciences, Constantine the Philosopher University, Nitra, 5 (2004), 43–50.
  • [5] H. Çakalli, S. Ersan, New types of continuity in 2-normed spaces, Filomat, 30(3) (2016), 525–532.
  • [6] P. Das, P. Kostyrko, W. Wilczy´nski, P. Malik, I and I-convergence of double sequences, Math. Slovaca, 58(5) (2008), 605–620.
  • [7] E. Dündar, B. Altay, I2-convergence of double sequences of functions, Electron. J. Math. Anal. Appl., 3(1) (2015), 111–121.
  • [8] E. Dündar, B. Altay, I2-convergence and I2-Cauchy of double sequences, Acta Math. Sci., 34B(2) (2014), 343–353.
  • [9] E. Dündar, B. Altay, I2-uniform convergence of double sequences of functions Filomat, 30(5) (2016), 1273–1281.
  • [10] E. Dündar, B. Altay, Multipliers for bounded I2-convergent of double sequences, Math. Comput. Modelling, 55(3-4) (2012), 1193–1198.
  • [11] E. Dündar, On some results of I2-convergence of double sequences of functions, Math. Anal. Sci. Appl. E-notes, 3(1) (2015), 44–52.
  • [12] E. Dündar. Ö. Talo, I2-convergence of double sequences of fuzzy numbers, Iran. J. Fuzzy Syst., 10(3) (2013), 37–50.
  • [13] E. Dündar, M. Arslan, S. Yegül, On I-Uniform Convergence of Sequences of Functions In 2-Normed Spaces, (Under Review).
  • [14] H. Fast, Sur la convergence statistique, Colloq. Math. 2 (1951), 241–244.
  • [15] J.A. Fridy, On statistical convergence, Analysis, 5 (1985), 301–313.
  • [16] S. Gahler, 2-metrische R¨aume und ihre topologische struktur, Math. Nachr. 26 (1963), 115–148.
  • [17] S. Gahler, 2-normed spaces, Math. Nachr. 28 (1964), 1–43.
  • [18] F. Gezer, S.Karakus¸, I and I convergent function sequences, Math. Commun. 10 (2005), 71–80.
  • [19] A. Gökhan, M. Güngör, M. Et, Statistical convergence of double sequences of real-valued functions, Int. Math. Forum, 2(8) (2007), 365–374.
  • [20] H. Gunawan, M. Mashadi, On finite dimensional 2-normed spaces, Soochow J. Math. 27(3) (2001), 321–329.
  • [21] M. Gürdal, S. Pehlivan, The statistical convergence in 2-Banach spaces, Thai J. Math. 2(1) (2004), 107–113.
  • [22] M. Gürdal, S. Pehlivan, Statistical convergence in 2-normed spaces, Southeast Asian Bull. Math., 33 (2009), 257–264.
  • [23] M. Gürdal, I.Açık On I-Cauchy sequences in 2-normed spaces, Math. Inequal. Appl. 11(2) (2008), 349–354.
  • [24] M. Gürdal, On ideal convergent sequences in 2-normed spaces, Thai J. Math. 4(1) (2006), 85–91.
  • [25] P. Kostyrko, T. Salat, W. Wilczynski, I-convergence, Real Anal. Exchange, 26(2) (2000), 669–686.
  • [26] M. Mursaleen, A. Alotaibi, On I-convergence in random 2-normed spaces, Math. Slovaca, 61(6) (2011), 933–940.
  • [27] N. Pancaroğlu, E. Dündar, F. Nuray, Wijsman I-Invariant Convergence of Sequences of Sets, Bull. Math. Anal. Appl., (Accepted - in press).
  • [28] N. Pancaroğlu, E. Dündar, U. Ulusu, Wijsman Lacunary I-Invariant Convergence of Sequences of Sets, (Under Review).
  • [29] S. Sarabadan, S. Talebi, Statistical convergence and ideal convergence of sequences of functions in 2-normed spaces, Internat. J. Math. Math. Sci. 2011 (2011), 10 pages.
  • [30] A. S¸ ahiner, M. Gürdal, S. Saltan, H. Gunawan, Ideal convergence in 2-normed spaces, Taiwanese J. Math. 11 (2007), 1477–1484.
  • [31] E. Savaş, M. Gürdal, Ideal Convergent Function Sequences in Random 2-Normed Spaces, Filomat, 30(3) (2016), 557–567.
  • [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] Ş . Tortop, E. Dündar, Wijsman I2 invariant convergence of Double Sequences of Sets, 9(4) (2018), 90–100.
  • [35] U. Ulusu, E. D¨undar, F. Nuray, Lacunary I2-Invariant Convergence and Some Properties, Internat. J. Anal. Appl., 16(3) (2018), 317–327.
  • [36] U. Ulusu, E. D¨undar, I-Lacunary Statistical Convergence of Sequences of Sets, Filomat, 28(8) (2013), 1567–1574.
  • [37] M. R. T¨urkmen and M. Çınar, Lambda Statistical Convergence in Fuzzy Normed Linear Spaces, J. Intel. Fuzzy Sys., 34(6) (2018), 4023–4030
  • [38] M. R. Türkmen and E. Dündar, On Lacunary Statistical Convergence of Double Sequences and Some Properties in Fuzzy Normed Spaces, J. Intel. Fuzzy Sys., DOI: 10.3233/JIFS-18841 (Pre-press).
  • [39] S. Yegül, E. Dündar, On Statistical Convergence of Sequences of Functions In 2-Normed Spaces, J. Class. Anal., (2017); 10(1):49–57.
  • [40] S. Yegül, E. Dündar, Statistical Convergence of Double Sequences of Functions and Some Properties In 2-Normed Spaces, Facta Univ. Ser. Math. Inform., 33(5) (2018), 705–719.

Yıl 2019, Cilt: 2 Sayı: 3, 130 - 137, 30.09.2019

Sevim Yegül Erdinç Dündar

https://doi.org/10.32323/ujma.606050
Cited By: 1

Öz

Kaynakça

  • [1] M. Arslan, E. Dündar, I-Convergence and I-Cauchy Sequence of Functions In 2-Normed Spaces, Konuralp J. Math., 6(1) (2018), 57–62.
  • [2] M. Arslan, E. Dündar, On I-Convergence of sequences of functions in 2-normed spaces, Southeast Asian Bull. Math., 42 (2018), 491–502.
  • [3] M. Arslan, E. Dündar, Rough convergence in 2-normed spaces, Bull. Math. Anal. Appl., 10(3) (2018), 1–9.
  • [4] V. Balaz, J. Cervenansky, P. Kostyrko, T. Salat, I-convergence and I-continuity of real functions, Acta Math., Faculty of Natural Sciences, Constantine the Philosopher University, Nitra, 5 (2004), 43–50.
  • [5] H. Çakalli, S. Ersan, New types of continuity in 2-normed spaces, Filomat, 30(3) (2016), 525–532.
  • [6] P. Das, P. Kostyrko, W. Wilczy´nski, P. Malik, I and I-convergence of double sequences, Math. Slovaca, 58(5) (2008), 605–620.
  • [7] E. Dündar, B. Altay, I2-convergence of double sequences of functions, Electron. J. Math. Anal. Appl., 3(1) (2015), 111–121.
  • [8] E. Dündar, B. Altay, I2-convergence and I2-Cauchy of double sequences, Acta Math. Sci., 34B(2) (2014), 343–353.
  • [9] E. Dündar, B. Altay, I2-uniform convergence of double sequences of functions Filomat, 30(5) (2016), 1273–1281.
  • [10] E. Dündar, B. Altay, Multipliers for bounded I2-convergent of double sequences, Math. Comput. Modelling, 55(3-4) (2012), 1193–1198.
  • [11] E. Dündar, On some results of I2-convergence of double sequences of functions, Math. Anal. Sci. Appl. E-notes, 3(1) (2015), 44–52.
  • [12] E. Dündar. Ö. Talo, I2-convergence of double sequences of fuzzy numbers, Iran. J. Fuzzy Syst., 10(3) (2013), 37–50.
  • [13] E. Dündar, M. Arslan, S. Yegül, On I-Uniform Convergence of Sequences of Functions In 2-Normed Spaces, (Under Review).
  • [14] H. Fast, Sur la convergence statistique, Colloq. Math. 2 (1951), 241–244.
  • [15] J.A. Fridy, On statistical convergence, Analysis, 5 (1985), 301–313.
  • [16] S. Gahler, 2-metrische R¨aume und ihre topologische struktur, Math. Nachr. 26 (1963), 115–148.
  • [17] S. Gahler, 2-normed spaces, Math. Nachr. 28 (1964), 1–43.
  • [18] F. Gezer, S.Karakus¸, I and I convergent function sequences, Math. Commun. 10 (2005), 71–80.
  • [19] A. Gökhan, M. Güngör, M. Et, Statistical convergence of double sequences of real-valued functions, Int. Math. Forum, 2(8) (2007), 365–374.
  • [20] H. Gunawan, M. Mashadi, On finite dimensional 2-normed spaces, Soochow J. Math. 27(3) (2001), 321–329.
  • [21] M. Gürdal, S. Pehlivan, The statistical convergence in 2-Banach spaces, Thai J. Math. 2(1) (2004), 107–113.
  • [22] M. Gürdal, S. Pehlivan, Statistical convergence in 2-normed spaces, Southeast Asian Bull. Math., 33 (2009), 257–264.
  • [23] M. Gürdal, I.Açık On I-Cauchy sequences in 2-normed spaces, Math. Inequal. Appl. 11(2) (2008), 349–354.
  • [24] M. Gürdal, On ideal convergent sequences in 2-normed spaces, Thai J. Math. 4(1) (2006), 85–91.
  • [25] P. Kostyrko, T. Salat, W. Wilczynski, I-convergence, Real Anal. Exchange, 26(2) (2000), 669–686.
  • [26] M. Mursaleen, A. Alotaibi, On I-convergence in random 2-normed spaces, Math. Slovaca, 61(6) (2011), 933–940.
  • [27] N. Pancaroğlu, E. Dündar, F. Nuray, Wijsman I-Invariant Convergence of Sequences of Sets, Bull. Math. Anal. Appl., (Accepted - in press).
  • [28] N. Pancaroğlu, E. Dündar, U. Ulusu, Wijsman Lacunary I-Invariant Convergence of Sequences of Sets, (Under Review).
  • [29] S. Sarabadan, S. Talebi, Statistical convergence and ideal convergence of sequences of functions in 2-normed spaces, Internat. J. Math. Math. Sci. 2011 (2011), 10 pages.
  • [30] A. S¸ ahiner, M. Gürdal, S. Saltan, H. Gunawan, Ideal convergence in 2-normed spaces, Taiwanese J. Math. 11 (2007), 1477–1484.
  • [31] E. Savaş, M. Gürdal, Ideal Convergent Function Sequences in Random 2-Normed Spaces, Filomat, 30(3) (2016), 557–567.
  • [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] Ş . Tortop, E. Dündar, Wijsman I2 invariant convergence of Double Sequences of Sets, 9(4) (2018), 90–100.
  • [35] U. Ulusu, E. D¨undar, F. Nuray, Lacunary I2-Invariant Convergence and Some Properties, Internat. J. Anal. Appl., 16(3) (2018), 317–327.
  • [36] U. Ulusu, E. D¨undar, I-Lacunary Statistical Convergence of Sequences of Sets, Filomat, 28(8) (2013), 1567–1574.
  • [37] M. R. T¨urkmen and M. Çınar, Lambda Statistical Convergence in Fuzzy Normed Linear Spaces, J. Intel. Fuzzy Sys., 34(6) (2018), 4023–4030
  • [38] M. R. Türkmen and E. Dündar, On Lacunary Statistical Convergence of Double Sequences and Some Properties in Fuzzy Normed Spaces, J. Intel. Fuzzy Sys., DOI: 10.3233/JIFS-18841 (Pre-press).
  • [39] S. Yegül, E. Dündar, On Statistical Convergence of Sequences of Functions In 2-Normed Spaces, J. Class. Anal., (2017); 10(1):49–57.
  • [40] S. Yegül, E. Dündar, Statistical Convergence of Double Sequences of Functions and Some Properties In 2-Normed Spaces, Facta Univ. Ser. Math. Inform., 33(5) (2018), 705–719.
Toplam 40 adet kaynakça vardır.

Ayrıntılar

Birincil Dil İngilizce
Konular Matematik
Bölüm Makaleler
Yazarlar

Sevim Yegül Bu kişi benim 0000-0002-0545-7486

Erdinç Dündar 0000-0002-0545-7486

Yayımlanma Tarihi 30 Eylül 2019
Gönderilme Tarihi 18 Ağustos 2019
Kabul Tarihi 12 Eylül 2019
Yayımlandığı Sayı Yıl 2019 Cilt: 2 Sayı: 3

Kaynak Göster

APA Yegül, S., & Dündar, E. (2019). $\mathcal{I}_2$-Convergence of Double Sequences of Functions in 2-Normed Spaces. Universal Journal of Mathematics and Applications, 2(3), 130-137. https://doi.org/10.32323/ujma.606050
AMA Yegül S, Dündar E. $\mathcal{I}_2$-Convergence of Double Sequences of Functions in 2-Normed Spaces. Univ. J. Math. Appl. Eylül 2019;2(3):130-137. doi:10.32323/ujma.606050
Chicago Yegül, Sevim, ve Erdinç Dündar. “$\mathcal{I}_2$-Convergence of Double Sequences of Functions in 2-Normed Spaces”. Universal Journal of Mathematics and Applications 2, sy. 3 (Eylül 2019): 130-37. https://doi.org/10.32323/ujma.606050.
EndNote Yegül S, Dündar E (01 Eylül 2019) $\mathcal{I}_2$-Convergence of Double Sequences of Functions in 2-Normed Spaces. Universal Journal of Mathematics and Applications 2 3 130–137.
IEEE S. Yegül ve E. Dündar, “$\mathcal{I}_2$-Convergence of Double Sequences of Functions in 2-Normed Spaces”, Univ. J. Math. Appl., c. 2, sy. 3, ss. 130–137, 2019, doi: 10.32323/ujma.606050.
ISNAD Yegül, Sevim - Dündar, Erdinç. “$\mathcal{I}_2$-Convergence of Double Sequences of Functions in 2-Normed Spaces”. Universal Journal of Mathematics and Applications 2/3 (Eylül 2019), 130-137. https://doi.org/10.32323/ujma.606050.
JAMA Yegül S, Dündar E. $\mathcal{I}_2$-Convergence of Double Sequences of Functions in 2-Normed Spaces. Univ. J. Math. Appl. 2019;2:130–137.
MLA Yegül, Sevim ve Erdinç Dündar. “$\mathcal{I}_2$-Convergence of Double Sequences of Functions in 2-Normed Spaces”. Universal Journal of Mathematics and Applications, c. 2, sy. 3, 2019, ss. 130-7, doi:10.32323/ujma.606050.
Vancouver Yegül S, Dündar E. $\mathcal{I}_2$-Convergence of Double Sequences of Functions in 2-Normed Spaces. Univ. J. Math. Appl. 2019;2(3):130-7.

Cited By

$\mathcal{I}_2$-Uniform Convergence of Double Sequences of Functions In $2$-Normed Spaces
Communications in Advanced Mathematical Sciences
https://doi.org/10.33434/cams.1177174
 Kapak Resmi İndir

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Universal Journal of Mathematics and Applications 

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