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ON ALMOST IDEAL CONVERGENCE WITH RESPECT TO AN ORLICZ FUNCTION

Year 2016, Volume: 4 Issue: 2, 87 - 94, 01.10.2016

Abstract

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.

References

  • [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.
Year 2016, Volume: 4 Issue: 2, 87 - 94, 01.10.2016

Abstract

References

  • [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.
There are 25 citations in total.

Details

Primary Language English
Subjects Engineering
Journal Section Articles
Authors

EMRAH EVREN Kara

MAHMUT Dastan This is me

MERVE Ilkhan

Publication Date October 1, 2016
Submission Date August 14, 2015
Published in Issue Year 2016 Volume: 4 Issue: 2

Cite

APA Kara, E. E., Dastan, M., & Ilkhan, M. (2016). ON ALMOST IDEAL CONVERGENCE WITH RESPECT TO AN ORLICZ FUNCTION. Konuralp Journal of Mathematics, 4(2), 87-94.
AMA Kara EE, Dastan M, Ilkhan M. ON ALMOST IDEAL CONVERGENCE WITH RESPECT TO AN ORLICZ FUNCTION. Konuralp J. Math. October 2016;4(2):87-94.
Chicago Kara, EMRAH EVREN, MAHMUT Dastan, and MERVE Ilkhan. “ON ALMOST IDEAL CONVERGENCE WITH RESPECT TO AN ORLICZ FUNCTION”. Konuralp Journal of Mathematics 4, no. 2 (October 2016): 87-94.
EndNote Kara EE, Dastan M, Ilkhan M (October 1, 2016) ON ALMOST IDEAL CONVERGENCE WITH RESPECT TO AN ORLICZ FUNCTION. Konuralp Journal of Mathematics 4 2 87–94.
IEEE E. E. Kara, M. Dastan, and M. Ilkhan, “ON ALMOST IDEAL CONVERGENCE WITH RESPECT TO AN ORLICZ FUNCTION”, Konuralp J. Math., vol. 4, no. 2, pp. 87–94, 2016.
ISNAD Kara, EMRAH EVREN et al. “ON ALMOST IDEAL CONVERGENCE WITH RESPECT TO AN ORLICZ FUNCTION”. Konuralp Journal of Mathematics 4/2 (October 2016), 87-94.
JAMA Kara EE, Dastan M, Ilkhan M. ON ALMOST IDEAL CONVERGENCE WITH RESPECT TO AN ORLICZ FUNCTION. Konuralp J. Math. 2016;4:87–94.
MLA Kara, EMRAH EVREN et al. “ON ALMOST IDEAL CONVERGENCE WITH RESPECT TO AN ORLICZ FUNCTION”. Konuralp Journal of Mathematics, vol. 4, no. 2, 2016, pp. 87-94.
Vancouver Kara EE, Dastan M, Ilkhan M. ON ALMOST IDEAL CONVERGENCE WITH RESPECT TO AN ORLICZ FUNCTION. Konuralp J. Math. 2016;4(2):87-94.
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