Research Article
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Year 2015, , 44 - 52, 15.05.2015
https://doi.org/10.36753/mathenot.421208

Abstract

References

  • [1] B. Altay, F. Başar, Some new spaces of double sequences, J. Math. Anal. Appl. 309(1) (2005), 70–90.
  • [2] A. Alotaibi, B. Hazarika, and S. A. Mohiuddine, On the ideal convergence of double sequences in locally solid Riesz spaces, Abstract and Applied Analysis, Volume 2014, Article ID 396254, (2014), 6 pages.
  • [3] V. Bal´az, J. Cervenansky, 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.
  • [4] M. Balcerzak, K. Dems, A. Komisarski, Statistical convergence and ideal convergence for sequences of functions, J. Math. Anal. Appl. 328 (2007), 715–729.
  • [5] C. Çakan, B. Altay, Statistically boundedness and statistical core of double sequences, J. Math. Anal. Appl. 317 (2006), 690–697.
  • [6] P. Das, P. Kostyrko, W. Wilczynski, P. Malik, I and I∗-convergence of double sequences, Math. Slovaca, 58 (2008), No. 5, 605–620.
  • [7] P. Das, P. Malik, On extremal I-limit points of double sequences, Tatra Mt. Math. Publ. 40 (2008), 91–102.
  • [8] E. Dündar, B. Altay, On some properties of I2-convergence and I2-Cauchy of double sequences, Gen. Math. Notes, 7(1) (2011), 1–12.
  • [9] E. Dündar, B. Altay, I2-convergence and I2-Cauchy of double sequences, (under communication).
  • [10] E. Dündar, B. Altay, I2-convergence of double sequences of functions, (under communication).
  • [11] H. Fast, Sur la convergenc statistique, Colloq. Math. 2 (1951), 241–244.
  • [12] J. A. Fridy, C. Orhan, Statistical limit superior and inferior, Proc. Amer. Math. Soc. 125 (1997), 3625–3631.
  • [13] J. A. Fridy, On statistical convergence, Analysis, 5 (1985), 301–313.
  • [14] J. A. Fridy, Statistical limit points, Proc. Amer. Math. Soc, 118 (1993), 1187–1192. [15] F. Gezer, S. Karakuş, I and I∗-convergent function sequences, Math. Commun. 10 (2005),71–80.
  • [16] A. Gökhan, M. Güngör, M. Et, Statistical convergence of double sequences of real-valued functions, Int. Math. Forum, 2(8) (2007), 365–374.
  • [17] M. Gürdal, A. Şahiner, Extremal I2-limit points of double sequences, Appl. Math. E-Notes, 2 (2008), 131-137.
  • [18] P. Kostyrko, T. Salat, W. Wilczyski, I-convergence, Real Anal. Exchange, 26(2) (2000), 669–686.
  • [19] P. Kostyrko, M. Macaj, T. Salat, M. Sleziak, I-convergence and extremal I-limit points, Math. Slovaca, 55 (2005), 443–464.
  • [20] V. Kumar, On I and I∗-convergence of double sequences, Math. Commun. 12 (2007), 171–181. [21] Mursaleen, O. H. H. Edely, Statistical convergence of double sequences, J. Math. Anal. Appl. 288 (2003), 223–231.
  • [22] M. Mursaleen and S. A. Mohiuddine, On ideal convergence of double sequences in probabilistic normed spaces, Math. Reports, 12(62)(4) (2010), 359–371.
  • [23] M. Mursaleen, S. A. Mohiuddine, and O. H. H. Edely, On the ideal convergence of double sequences in intuitionistic fuzzy normed spaces, Comput. Math. Appl. 59(2) (2010), 603–611.
  • [24] S. A. Mohiuddine, A. Alotaibi, and S. M. Alsulami, Ideal convergence of double sequences in random 2-normed spaces, Adv. Difference Equ. vol. 2012, article 149, (2012), 8 pages.
  • [25] A. Nabiev, S. Pehlivan, M. G¨urdal, On I-Cauchy sequence, Taiwanese J. Math. 11(2) (2007), 569–576.
  • [26] F. Nuray, W. H. Ruckle, Generalized statistical convergence and convergence free spaces, J. Math. Anal. Appl. 245 (2000), 513–527.
  • [27] A. Pringsheim, Zur theorie der zweifach unendlichen Zahlenfolgen, Math. Ann. 53 (1900), 289–321.
  • [28] D. Rath, B. C. Tripaty, On statistically convergence and statistically Cauchy sequences, Indian J. Pure Appl. Math. 25(4) (1994), 381–386.
  • [29] T. Salat, On statistically convergent sequences of real numbers, Math. Slovaca, 30 (1980), 139–150.
  • [30] I. J. Schoenberg, The integrability of certain functions and related summability methods, Amer. Math. Monthly 66 (1959), 361–375.
  • [31] B. Tripathy, B. C. Tripathy, On I-convergent double sequences, Soochow J. Math. 31 (2005), 549–560.

ON SOME RESULTS OF I_2-CONVERGENCE OF DOUBLE SEQUENCES OF FUNCTIONS

Year 2015, , 44 - 52, 15.05.2015
https://doi.org/10.36753/mathenot.421208

Abstract

In this work, we investigate some results of I2-convergence of double
sequences of real valued functions and prove a decomposition theorem.

References

  • [1] B. Altay, F. Başar, Some new spaces of double sequences, J. Math. Anal. Appl. 309(1) (2005), 70–90.
  • [2] A. Alotaibi, B. Hazarika, and S. A. Mohiuddine, On the ideal convergence of double sequences in locally solid Riesz spaces, Abstract and Applied Analysis, Volume 2014, Article ID 396254, (2014), 6 pages.
  • [3] V. Bal´az, J. Cervenansky, 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.
  • [4] M. Balcerzak, K. Dems, A. Komisarski, Statistical convergence and ideal convergence for sequences of functions, J. Math. Anal. Appl. 328 (2007), 715–729.
  • [5] C. Çakan, B. Altay, Statistically boundedness and statistical core of double sequences, J. Math. Anal. Appl. 317 (2006), 690–697.
  • [6] P. Das, P. Kostyrko, W. Wilczynski, P. Malik, I and I∗-convergence of double sequences, Math. Slovaca, 58 (2008), No. 5, 605–620.
  • [7] P. Das, P. Malik, On extremal I-limit points of double sequences, Tatra Mt. Math. Publ. 40 (2008), 91–102.
  • [8] E. Dündar, B. Altay, On some properties of I2-convergence and I2-Cauchy of double sequences, Gen. Math. Notes, 7(1) (2011), 1–12.
  • [9] E. Dündar, B. Altay, I2-convergence and I2-Cauchy of double sequences, (under communication).
  • [10] E. Dündar, B. Altay, I2-convergence of double sequences of functions, (under communication).
  • [11] H. Fast, Sur la convergenc statistique, Colloq. Math. 2 (1951), 241–244.
  • [12] J. A. Fridy, C. Orhan, Statistical limit superior and inferior, Proc. Amer. Math. Soc. 125 (1997), 3625–3631.
  • [13] J. A. Fridy, On statistical convergence, Analysis, 5 (1985), 301–313.
  • [14] J. A. Fridy, Statistical limit points, Proc. Amer. Math. Soc, 118 (1993), 1187–1192. [15] F. Gezer, S. Karakuş, I and I∗-convergent function sequences, Math. Commun. 10 (2005),71–80.
  • [16] A. Gökhan, M. Güngör, M. Et, Statistical convergence of double sequences of real-valued functions, Int. Math. Forum, 2(8) (2007), 365–374.
  • [17] M. Gürdal, A. Şahiner, Extremal I2-limit points of double sequences, Appl. Math. E-Notes, 2 (2008), 131-137.
  • [18] P. Kostyrko, T. Salat, W. Wilczyski, I-convergence, Real Anal. Exchange, 26(2) (2000), 669–686.
  • [19] P. Kostyrko, M. Macaj, T. Salat, M. Sleziak, I-convergence and extremal I-limit points, Math. Slovaca, 55 (2005), 443–464.
  • [20] V. Kumar, On I and I∗-convergence of double sequences, Math. Commun. 12 (2007), 171–181. [21] Mursaleen, O. H. H. Edely, Statistical convergence of double sequences, J. Math. Anal. Appl. 288 (2003), 223–231.
  • [22] M. Mursaleen and S. A. Mohiuddine, On ideal convergence of double sequences in probabilistic normed spaces, Math. Reports, 12(62)(4) (2010), 359–371.
  • [23] M. Mursaleen, S. A. Mohiuddine, and O. H. H. Edely, On the ideal convergence of double sequences in intuitionistic fuzzy normed spaces, Comput. Math. Appl. 59(2) (2010), 603–611.
  • [24] S. A. Mohiuddine, A. Alotaibi, and S. M. Alsulami, Ideal convergence of double sequences in random 2-normed spaces, Adv. Difference Equ. vol. 2012, article 149, (2012), 8 pages.
  • [25] A. Nabiev, S. Pehlivan, M. G¨urdal, On I-Cauchy sequence, Taiwanese J. Math. 11(2) (2007), 569–576.
  • [26] F. Nuray, W. H. Ruckle, Generalized statistical convergence and convergence free spaces, J. Math. Anal. Appl. 245 (2000), 513–527.
  • [27] A. Pringsheim, Zur theorie der zweifach unendlichen Zahlenfolgen, Math. Ann. 53 (1900), 289–321.
  • [28] D. Rath, B. C. Tripaty, On statistically convergence and statistically Cauchy sequences, Indian J. Pure Appl. Math. 25(4) (1994), 381–386.
  • [29] T. Salat, On statistically convergent sequences of real numbers, Math. Slovaca, 30 (1980), 139–150.
  • [30] I. J. Schoenberg, The integrability of certain functions and related summability methods, Amer. Math. Monthly 66 (1959), 361–375.
  • [31] B. Tripathy, B. C. Tripathy, On I-convergent double sequences, Soochow J. Math. 31 (2005), 549–560.
There are 29 citations in total.

Details

Primary Language English
Journal Section Articles
Authors

Erdinç Dündar This is me

Publication Date May 15, 2015
Submission Date July 20, 2014
Published in Issue Year 2015

Cite

APA Dündar, E. (2015). ON SOME RESULTS OF I_2-CONVERGENCE OF DOUBLE SEQUENCES OF FUNCTIONS. Mathematical Sciences and Applications E-Notes, 3(1), 44-52. https://doi.org/10.36753/mathenot.421208
AMA Dündar E. ON SOME RESULTS OF I_2-CONVERGENCE OF DOUBLE SEQUENCES OF FUNCTIONS. Math. Sci. Appl. E-Notes. May 2015;3(1):44-52. doi:10.36753/mathenot.421208
Chicago Dündar, Erdinç. “ON SOME RESULTS OF I_2-CONVERGENCE OF DOUBLE SEQUENCES OF FUNCTIONS”. Mathematical Sciences and Applications E-Notes 3, no. 1 (May 2015): 44-52. https://doi.org/10.36753/mathenot.421208.
EndNote Dündar E (May 1, 2015) ON SOME RESULTS OF I_2-CONVERGENCE OF DOUBLE SEQUENCES OF FUNCTIONS. Mathematical Sciences and Applications E-Notes 3 1 44–52.
IEEE E. Dündar, “ON SOME RESULTS OF I_2-CONVERGENCE OF DOUBLE SEQUENCES OF FUNCTIONS”, Math. Sci. Appl. E-Notes, vol. 3, no. 1, pp. 44–52, 2015, doi: 10.36753/mathenot.421208.
ISNAD Dündar, Erdinç. “ON SOME RESULTS OF I_2-CONVERGENCE OF DOUBLE SEQUENCES OF FUNCTIONS”. Mathematical Sciences and Applications E-Notes 3/1 (May 2015), 44-52. https://doi.org/10.36753/mathenot.421208.
JAMA Dündar E. ON SOME RESULTS OF I_2-CONVERGENCE OF DOUBLE SEQUENCES OF FUNCTIONS. Math. Sci. Appl. E-Notes. 2015;3:44–52.
MLA Dündar, Erdinç. “ON SOME RESULTS OF I_2-CONVERGENCE OF DOUBLE SEQUENCES OF FUNCTIONS”. Mathematical Sciences and Applications E-Notes, vol. 3, no. 1, 2015, pp. 44-52, doi:10.36753/mathenot.421208.
Vancouver Dündar E. ON SOME RESULTS OF I_2-CONVERGENCE OF DOUBLE SEQUENCES OF FUNCTIONS. Math. Sci. Appl. E-Notes. 2015;3(1):44-52.

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