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

Year 2015, Volume: 3 Issue: 1 , 44 - 52 , 15.05.2015

Erdinç Dündar

https://doi.org/10.36753/mathenot.421208

Cited By: 3

https://izlik.org/JA44TJ57KH

Abstract

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

Keywords

Ideal , Double Sequences , Double Sequences of Functions , I-Convergence

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.