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

Year 2019, , 130 - 137, 30.09.2019
https://doi.org/10.32323/ujma.606050

Abstract

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.

References

  • [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.
Year 2019, , 130 - 137, 30.09.2019
https://doi.org/10.32323/ujma.606050

Abstract

References

  • [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.
There are 40 citations in total.

Details

Primary Language English
Subjects Mathematical Sciences
Journal Section Articles
Authors

Sevim Yegül This is me 0000-0002-0545-7486

Erdinç Dündar 0000-0002-0545-7486

Publication Date September 30, 2019
Submission Date August 18, 2019
Acceptance Date September 12, 2019
Published in Issue Year 2019

Cite

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. September 2019;2(3):130-137. doi:10.32323/ujma.606050
Chicago Yegül, Sevim, and Erdinç Dündar. “$\mathcal{I}_2$-Convergence of Double Sequences of Functions in 2-Normed Spaces”. Universal Journal of Mathematics and Applications 2, no. 3 (September 2019): 130-37. https://doi.org/10.32323/ujma.606050.
EndNote Yegül S, Dündar E (September 1, 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 and E. Dündar, “$\mathcal{I}_2$-Convergence of Double Sequences of Functions in 2-Normed Spaces”, Univ. J. Math. Appl., vol. 2, no. 3, pp. 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 (September 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 and Erdinç Dündar. “$\mathcal{I}_2$-Convergence of Double Sequences of Functions in 2-Normed Spaces”. Universal Journal of Mathematics and Applications, vol. 2, no. 3, 2019, pp. 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.

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