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$\mathcal{I}$-Convergence and $\mathcal{I}$-Cauchy Sequence of Functions In 2-Normed Spaces

Yıl 2018, Cilt: 6 Sayı: 1, 57 - 62, 15.04.2018

Öz

In this paper, we study concepts of $\mathcal{I}$-convergence, $\mathcal{I}^*$-convergence, $\mathcal{I}$-Cauchy and $\mathcal{I}^*$-Cauchy sequences of functions and investigate relationships between them and some properties in $2$-normed spaces.

Kaynakça

  • [1] V. Balaz, J. C ervenansky, P. Kostyrko, T. Salat, I-convergence and I-continuity of real functions, Acta Mathematica, Faculty of Natural Sciences, Constantine the Philosopher University, Nitra, 5 (2004), 43–50.
  • [2] M. Balcerzak, K. Dems, A. Komisarski, Statistical convergence and ideal convergence for sequences of functions, J. Math. Anal. Appl., 328 (2007), 715-729.
  • [3] H. C¸ akallı and S. Ersan, New types of continuity in 2-normed spaces, Filomat, 30(3) (2016), 525–532.
  • [4] O. Duman, C. Orhan, m-statistically convergent function sequences, Czechoslovak Mathematical Journal, 54(129) (2004), 413–422.
  • [5] E. Dündar, B. Altay, I2-convergence of double sequences of functions, Electronic Journal of Mathematical Analysis and Applications, 3(1) (2015), 111–121.
  • [6] E. Dündar, B. Altay, I2-uniform convergence of double sequences of functions, Filomat, 30(5) (2016), 1273–1281.
  • [7] E. Dündar, On some results of I2-convergence of double sequences of functions, Mathematical Analysis Sciences and Applications E-notes, 3(1) (2015), 44–52.
  • [8] H. Fast, Sur la convergence statistique, Colloq. Math., 2 (1951), 241–244.
  • [9] J.A. Fridy, On statistical convergence, Analysis, 5 (1985), 301–313.
  • [10] S. G¨ahler, 2-metrische R¨aume und ihre topologische struktur, Math. Nachr., 26 (1963), 115–148.
  • [11] S. G¨ahler, 2-normed spaces, Math. Nachr., 28 (1964), 1–43.
  • [12] F. Gezer, S. Karakus¸, I and I convergent function sequences, Math. Commun., 10 (2005), 71-80.
  • [13] A. Gökhan, M. Güngör and M. Et, Statistical convergence of double sequences of real-valued functions, Int. Math. Forum, 2(8) (2007), 365-374.
  • [14] H. Gunawan, M. Mashadi, On n-normed spaces, Int. J. Math. Math. Sci., 27 (10) (2001), 631–639.
  • [15] H. Gunawan, M. Mashadi, On finite dimensional 2-normed spaces, Soochow J. Math., 27(3) (2001), 321–329.
  • [16] M. Gürdal, S. Pehlivan, The statistical convergence in 2-Banach spaces, Thai J. Math., 2(1) (2004), 107–113.
  • [17] M. Gürdal, S. Pehlivan, Statistical convergence in 2-normed spaces, Southeast Asian Bulletin of Mathematics, 33 (2009), 257–264. [18] M. Gürdal, I. Açık, On I-Cauchy sequences in 2-normed spaces, Math. Inequal. Appl., 11(2) (2008), 349–354.
  • [19] M. Gürdal, On ideal convergent sequences in 2-normed spaces, Thai J. Math., 4(1) (2006), 85–91.
  • [20] P. Kostyrko, T. ˘ Sal´at, W. Wilczy´nski, I-convergence, Real Anal. Exchange, 26(2) (2000), 669–686.
  • [21] M. Mursaleen, S.A. Mohiuddine, On ideal convergence in probabilistic normed spaces, Math. Slovaca, 62 (2012), 49-62.
  • [22] M. Mursaleen, A. Alotaibi, On I-convergence in random 2-normed spaces, Math. Slovaca, 61 (6) (2011), 933–940.
  • [23] A. Nabiev, S. Pehlivan and M. G¨urdal, On I-Cauchy sequences, Taiwanese J. Math. 11(2) (2007), 569–576.
  • [24] F. Nuray, W.H. Ruckle, Generalized statistical convergence and convergence free spaces, J. Math. Anal. Appl., 245 (2000), 513–527.
  • [25] 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.
  • [26] E. Savas¸, M. G¨urdal, Ideal Convergent Function Sequences in Random 2-Normed Spaces, Filomat, 30(3) (2016), 557–567.
  • [27] I.J. Schoenberg, The integrability of certain functions and related summability methods, Amer. Math. Monthly, 66 (1959), 361–375.
  • [28] A. Sharma, K. Kumar, Statistical convergence in probabilistic 2-normed spaces, Mathematical Sciences, 2(4) (2008), 373–390.
  • [29] A. S¸ ahiner, M. G¨urdal, S. Saltan, H. Gunawan, Ideal convergence in 2-normed spaces, Taiwanese J. Math., 11 (2007), 1477–1484.
  • [30] B.C. Tripathy, M. Sen, S. Nath, I-convergence in probabilistic n-normed space, Soft Comput., 16 (2012), 1021–1027.
  • [31] S. Yegül, E. Dündar, On Statistical Convergence of Sequences of Functions In 2-Normed Spaces, Journal of Classical Analysis, 10(1) (2017), 49–57.
Yıl 2018, Cilt: 6 Sayı: 1, 57 - 62, 15.04.2018

Öz

Kaynakça

  • [1] V. Balaz, J. C ervenansky, P. Kostyrko, T. Salat, I-convergence and I-continuity of real functions, Acta Mathematica, Faculty of Natural Sciences, Constantine the Philosopher University, Nitra, 5 (2004), 43–50.
  • [2] M. Balcerzak, K. Dems, A. Komisarski, Statistical convergence and ideal convergence for sequences of functions, J. Math. Anal. Appl., 328 (2007), 715-729.
  • [3] H. C¸ akallı and S. Ersan, New types of continuity in 2-normed spaces, Filomat, 30(3) (2016), 525–532.
  • [4] O. Duman, C. Orhan, m-statistically convergent function sequences, Czechoslovak Mathematical Journal, 54(129) (2004), 413–422.
  • [5] E. Dündar, B. Altay, I2-convergence of double sequences of functions, Electronic Journal of Mathematical Analysis and Applications, 3(1) (2015), 111–121.
  • [6] E. Dündar, B. Altay, I2-uniform convergence of double sequences of functions, Filomat, 30(5) (2016), 1273–1281.
  • [7] E. Dündar, On some results of I2-convergence of double sequences of functions, Mathematical Analysis Sciences and Applications E-notes, 3(1) (2015), 44–52.
  • [8] H. Fast, Sur la convergence statistique, Colloq. Math., 2 (1951), 241–244.
  • [9] J.A. Fridy, On statistical convergence, Analysis, 5 (1985), 301–313.
  • [10] S. G¨ahler, 2-metrische R¨aume und ihre topologische struktur, Math. Nachr., 26 (1963), 115–148.
  • [11] S. G¨ahler, 2-normed spaces, Math. Nachr., 28 (1964), 1–43.
  • [12] F. Gezer, S. Karakus¸, I and I convergent function sequences, Math. Commun., 10 (2005), 71-80.
  • [13] A. Gökhan, M. Güngör and M. Et, Statistical convergence of double sequences of real-valued functions, Int. Math. Forum, 2(8) (2007), 365-374.
  • [14] H. Gunawan, M. Mashadi, On n-normed spaces, Int. J. Math. Math. Sci., 27 (10) (2001), 631–639.
  • [15] H. Gunawan, M. Mashadi, On finite dimensional 2-normed spaces, Soochow J. Math., 27(3) (2001), 321–329.
  • [16] M. Gürdal, S. Pehlivan, The statistical convergence in 2-Banach spaces, Thai J. Math., 2(1) (2004), 107–113.
  • [17] M. Gürdal, S. Pehlivan, Statistical convergence in 2-normed spaces, Southeast Asian Bulletin of Mathematics, 33 (2009), 257–264. [18] M. Gürdal, I. Açık, On I-Cauchy sequences in 2-normed spaces, Math. Inequal. Appl., 11(2) (2008), 349–354.
  • [19] M. Gürdal, On ideal convergent sequences in 2-normed spaces, Thai J. Math., 4(1) (2006), 85–91.
  • [20] P. Kostyrko, T. ˘ Sal´at, W. Wilczy´nski, I-convergence, Real Anal. Exchange, 26(2) (2000), 669–686.
  • [21] M. Mursaleen, S.A. Mohiuddine, On ideal convergence in probabilistic normed spaces, Math. Slovaca, 62 (2012), 49-62.
  • [22] M. Mursaleen, A. Alotaibi, On I-convergence in random 2-normed spaces, Math. Slovaca, 61 (6) (2011), 933–940.
  • [23] A. Nabiev, S. Pehlivan and M. G¨urdal, On I-Cauchy sequences, Taiwanese J. Math. 11(2) (2007), 569–576.
  • [24] F. Nuray, W.H. Ruckle, Generalized statistical convergence and convergence free spaces, J. Math. Anal. Appl., 245 (2000), 513–527.
  • [25] 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.
  • [26] E. Savas¸, M. G¨urdal, Ideal Convergent Function Sequences in Random 2-Normed Spaces, Filomat, 30(3) (2016), 557–567.
  • [27] I.J. Schoenberg, The integrability of certain functions and related summability methods, Amer. Math. Monthly, 66 (1959), 361–375.
  • [28] A. Sharma, K. Kumar, Statistical convergence in probabilistic 2-normed spaces, Mathematical Sciences, 2(4) (2008), 373–390.
  • [29] A. S¸ ahiner, M. G¨urdal, S. Saltan, H. Gunawan, Ideal convergence in 2-normed spaces, Taiwanese J. Math., 11 (2007), 1477–1484.
  • [30] B.C. Tripathy, M. Sen, S. Nath, I-convergence in probabilistic n-normed space, Soft Comput., 16 (2012), 1021–1027.
  • [31] S. Yegül, E. Dündar, On Statistical Convergence of Sequences of Functions In 2-Normed Spaces, Journal of Classical Analysis, 10(1) (2017), 49–57.
Toplam 30 adet kaynakça vardır.

Ayrıntılar

Birincil Dil İngilizce
Konular Mühendislik
Bölüm Articles
Yazarlar

Mukaddes Arslan

Erdinç Dündar Bu kişi benim

Yayımlanma Tarihi 15 Nisan 2018
Gönderilme Tarihi 15 Ağustos 2017
Yayımlandığı Sayı Yıl 2018 Cilt: 6 Sayı: 1

Kaynak Göster

APA Arslan, M., & Dündar, E. (2018). $\mathcal{I}$-Convergence and $\mathcal{I}$-Cauchy Sequence of Functions In 2-Normed Spaces. Konuralp Journal of Mathematics, 6(1), 57-62.
AMA Arslan M, Dündar E. $\mathcal{I}$-Convergence and $\mathcal{I}$-Cauchy Sequence of Functions In 2-Normed Spaces. Konuralp J. Math. Nisan 2018;6(1):57-62.
Chicago Arslan, Mukaddes, ve Erdinç Dündar. “$\mathcal{I}$-Convergence and $\mathcal{I}$-Cauchy Sequence of Functions In 2-Normed Spaces”. Konuralp Journal of Mathematics 6, sy. 1 (Nisan 2018): 57-62.
EndNote Arslan M, Dündar E (01 Nisan 2018) $\mathcal{I}$-Convergence and $\mathcal{I}$-Cauchy Sequence of Functions In 2-Normed Spaces. Konuralp Journal of Mathematics 6 1 57–62.
IEEE M. Arslan ve E. Dündar, “$\mathcal{I}$-Convergence and $\mathcal{I}$-Cauchy Sequence of Functions In 2-Normed Spaces”, Konuralp J. Math., c. 6, sy. 1, ss. 57–62, 2018.
ISNAD Arslan, Mukaddes - Dündar, Erdinç. “$\mathcal{I}$-Convergence and $\mathcal{I}$-Cauchy Sequence of Functions In 2-Normed Spaces”. Konuralp Journal of Mathematics 6/1 (Nisan 2018), 57-62.
JAMA Arslan M, Dündar E. $\mathcal{I}$-Convergence and $\mathcal{I}$-Cauchy Sequence of Functions In 2-Normed Spaces. Konuralp J. Math. 2018;6:57–62.
MLA Arslan, Mukaddes ve Erdinç Dündar. “$\mathcal{I}$-Convergence and $\mathcal{I}$-Cauchy Sequence of Functions In 2-Normed Spaces”. Konuralp Journal of Mathematics, c. 6, sy. 1, 2018, ss. 57-62.
Vancouver Arslan M, Dündar E. $\mathcal{I}$-Convergence and $\mathcal{I}$-Cauchy Sequence of Functions In 2-Normed Spaces. Konuralp J. Math. 2018;6(1):57-62.
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