ON ALMOST IDEAL CONVERGENCE WITH RESPECT TO AN ORLICZ FUNCTION

Yıl 2016, Cilt: 4 Sayı: 2, 87 - 94, 01.10.2016

EMRAH EVREN Kara MAHMUT Dastan MERVE Ilkhan

Öz

In this article, we define new classes of ideal convergent and ideal bounded sequence spaces combining an infinite matrix, an Orlicz function and invariant mean. We investigate some linear topological structures and algebraic properties of the resulting spaces. Also we find out some relations related to these spaces.

Anahtar Kelimeler

Invariant means, ideal convergence, Orlicz functions

Kaynakça

• [1] H. Fast, Sur la convergence statistique, Colloq. Math. 2 (1951), 241{244.
• [2] I. J. Schoenberg, The integrability of certain functions and related summability methods, Amer. Math. Monthly 66 (1959), 361{375. [3] P. Kostyrko, T. Salat and W. Wilczynski, I-convergence, Real Anal. Exchange 26(2), (2000-2001) 669-685.
• [4] P. Kostyrko, M. Macaj, T. Salat and M. Sleziak, I-convergence and external I-limit points, Math. Slovaca 55(4) (2005), 443{464.
• [5] T. Salat, B. C. Tripathy and M. Ziman, On some properties of I-convergence, Tatra Mt. Math. Publ. 28 (2004), 279{286.
• [6] B. C. Tripathy, B. Hazarika, Paranorm I-convergent sequence spaces, Math. Slovaca 59(4) (2009), 485{494.
• [7] B. C. Tripathy, B. Hazarika, I-monotonic and I-convergent sequences, Kyungpook Math. J. 51(2) (2011), 233{239.
• [8] A. Sahiner, M. Gurdal, S. Saltan and H. Gunawan, Ideal convergence in 2-normed spaces, Taiwanese J. Math. 11(5) (2007), 1477{1484.
• [9] M. Gurdal, On ideal convergent sequences in 2-normed spaces, Thai J. Math. 4(1) (2006), 85{91.
• [10] M. Gurdal, M. B. Huban, On I-convergence of double sequences in the Topology induced by random 2-norms, Mat. Vesnik 66(1) (2014), 73-83.
• [11] P. Das, Some further results on ideal convergence in topological spaces, Topology Appl. 159(10-11), (2012) 2621{2626.
• [12] B. K. Lahiri, P. Das, I and I*-convergence in topological spaces, Math. Bohem. 130(2) (2005), 153-160.
• [13] P. Schaefer, Innite matrices and invariant means, Proc. Amer. Math. Soc. 36 (1972), 104- 110.
• [14] G. G. Lorentz, A contribution to the theory of divergent series, Acta Math. 80(1) (1948), 167-190. [15] I. J. Maddox, Spaces of strongly summable sequences, Q. J. Math. 18 (1967), 345-355.
• [16] M. A. Krasnoselskii, Y. B. Rutitsky, Convex function and Orlicz spaces, P.Noordho, Groningen, The Netherlands, 1961.
• [17] J. Lindenstrauss, L. Tzafriri, On Orlicz sequence spaces, Israel J. Math. 10(3) (1971), 379- 390.
• [18] P. K. Kamptan, M. Gupta, Sequence spaces and series, Marcel Dekker, New York, 1980.
• [19] S. D. Parashar, B. Choudhary, Sequence spaces dened by Orlicz functions, Indian J. Pure Appl. Math. 25(4) (1994), 419-428.
• [20] V. Karakaya, Some new sequence spaces dened by a sequence of Orlicz functions, Taiwanese J. Math. 9(4) (2005), 617-627.
• [21] B. C. Tripathy, M. Et and Y. AltIn, Generalized difference sequences spaces dened by Orlicz function in a locally convex space, J. Anal. Appl. 3(1) (2003), 175{192.
• [22] M. Gungor, M. Et,
  m-strongly almost summable sequences dened by Orlicz functions, Indian J. Pure Appl. Math. 34(8) (2003), 1141-1151.
• [23] A. Esi, Strongly almost summable sequence spaces in 2-normed spaces dened by ideal convergence and an Orlicz function, Stud. Univ. Babes-Bolyai Math. 57(1) (2012), 75-82.
• [24] B. Hazarika, Strongly almost ideal convergent sequence spaces in a locally convex space dened by Musielak-Orlicz function, Iran. J. Math. Sci. Inform. 9(2) (2014), 15-35.
• [25] A. Sahiner, On I-lacunary strong convergence in 2-normed spaces, Int. J. Contempt. Math. Sciences 2(20) (2007), 991-998.
• [26] B. Hazarika, K. Tamang and B. K. Singh, On paranormed Zweier ideal convergent sequence spaces dened by Orlicz function, J. Egyptian Math. Soc. http://dx.doi.org/10.1016/j.joems.2013.08.005, (2013).
• [27] E. E. Kara, M. Ilkhan, Lacunary I-convergent and lacunary I-bounded sequence spaces dened by an Orlicz function, Electron. J. Math. Anal. Appl. 4(2) (2016), 150-159.