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Mλ- Toplanabilme Metoduyla Tanımlanan Bazı Yeni İdeal Yakınsak Dizi Uzayları

Year 2017, Volume: 38 Supplement Issue 4, 130 - 137, 08.12.2017

Nazlım Deniz Aral Şükran Konca

https://doi.org/10.17776/csj.363614

Abstract

Bu çalışmada Nörlund
metodunun bir genelleşmesi olarak P.N. Natarajan [On the -method of summability, Analysis] tarafından tanımlanan -toplanabilme metodu kullanılarak bazı ideal yakınsak dizi
uzayları tanımlanmıştır. Ayrıca, bu uzayların bazı topolojik özellikleri
incelenmiştir.

Keywords

-yakınsaklık Orlicz fonksiyonu -toplanabilme metodu dizi uzayı

References

  • [1]. Birnbaum Z., Orlicz W. Uber die Verallgemeinerung des Begriffes der zueinander Konjugierten Potenzen, Studia Mathematica, 1931; 3: 1-67.
  • [2]. Krasnosel'skii M.A., Rutickii Y.B. Convex Functions and Orlicz Spaces, P. Noordhoff Ltd., Groningen, Netherlands, 1961.
  • [3]. Lindberg, K., On subspaces of Orlicz sequence spaces, Studia Mathematica, 1973; 45 (2):119-146.
  • [4]. Lindenstrauss J., Tzafriri L. On Orlicz Sequence Spaces, Israel Journal of Mathematics, 1971; 10 (3): 379-390.
  • [5]. Parashar S.D., Choudhary B. Sequence Spaces Defined by Orlicz Function, Indian Journal Pure and Applied Mathematics, 1994; 24 (4): 419-428.
  • [6]. Kostyrko P., Wilczynski W., Salat T. I-convergence, Real Analysis Exchange, 2000; 26 (2): 669-686.
  • [7]. Tripathy B.C., Hazarika B. Some I-convergent sequence spaces defined by Orlicz functions, Acta Mathematicae Applicatae Sinica, 2011; 27 (1): 149-154.
  • [8]. Savas E. On some new sequence spaces in 2-normed spaces using ideal convergence and an Orlicz function, Journal of Inequalities and Applications, 2010; Article ID 482392, 8 pages.
  • [9]. Mursaleen M., Sharma S.K. Spaces of Ideal Sequences, Hindawi, 2014; Artical ID 134534, 6 pages.
  • [10]. Savaş E., Das P. A generalized statistical convergence via ideals, Application Letters, 2011; 24 (6): 826-830.
  • [11]. Salat T., Tripathy B.C., Ziman M. On some properties of I-convergence, Tatra Mountains Mathematical Publications, 2004; 28: 279-286.
  • [12]. Natarajan P.N. On the method of summability, Analysis, 2013; {33}: 51-56.
  • [13]. Aral N.D., Küçükaslan M. On -statistical Convergence, Journal of Mathematical Analysis, 2016; 7 (2): 37-46.
  • [14]. Kamrhan P.K., Gupta M. Sequence spaces and series Marcel Dekker, New York, 1981.
  • [15]. Maddox I.J. Elements of Functional Analysis Cambridge Univ. Press, Cambridge, 1970.

On Some New Ideal Convergent Sequence Spaces of -Method of Summability

Year 2017, Volume: 38 Supplement Issue 4, 130 - 137, 08.12.2017

Nazlım Deniz Aral Şükran Konca

https://doi.org/10.17776/csj.363614

Abstract

In the
present work, we introduce some ideal convergent sequence spaces by using  - summability method which is defined by P. N. Natarajan [On
the -method of summability, Analysis] as a typically
generalization of Nörlund method. Further, we examine some of their topological
properties.

Keywords

-convergence Orlicz function -method of summability sequence space

References

  • [1]. Birnbaum Z., Orlicz W. Uber die Verallgemeinerung des Begriffes der zueinander Konjugierten Potenzen, Studia Mathematica, 1931; 3: 1-67.
  • [2]. Krasnosel'skii M.A., Rutickii Y.B. Convex Functions and Orlicz Spaces, P. Noordhoff Ltd., Groningen, Netherlands, 1961.
  • [3]. Lindberg, K., On subspaces of Orlicz sequence spaces, Studia Mathematica, 1973; 45 (2):119-146.
  • [4]. Lindenstrauss J., Tzafriri L. On Orlicz Sequence Spaces, Israel Journal of Mathematics, 1971; 10 (3): 379-390.
  • [5]. Parashar S.D., Choudhary B. Sequence Spaces Defined by Orlicz Function, Indian Journal Pure and Applied Mathematics, 1994; 24 (4): 419-428.
  • [6]. Kostyrko P., Wilczynski W., Salat T. I-convergence, Real Analysis Exchange, 2000; 26 (2): 669-686.
  • [7]. Tripathy B.C., Hazarika B. Some I-convergent sequence spaces defined by Orlicz functions, Acta Mathematicae Applicatae Sinica, 2011; 27 (1): 149-154.
  • [8]. Savas E. On some new sequence spaces in 2-normed spaces using ideal convergence and an Orlicz function, Journal of Inequalities and Applications, 2010; Article ID 482392, 8 pages.
  • [9]. Mursaleen M., Sharma S.K. Spaces of Ideal Sequences, Hindawi, 2014; Artical ID 134534, 6 pages.
  • [10]. Savaş E., Das P. A generalized statistical convergence via ideals, Application Letters, 2011; 24 (6): 826-830.
  • [11]. Salat T., Tripathy B.C., Ziman M. On some properties of I-convergence, Tatra Mountains Mathematical Publications, 2004; 28: 279-286.
  • [12]. Natarajan P.N. On the method of summability, Analysis, 2013; {33}: 51-56.
  • [13]. Aral N.D., Küçükaslan M. On -statistical Convergence, Journal of Mathematical Analysis, 2016; 7 (2): 37-46.
  • [14]. Kamrhan P.K., Gupta M. Sequence spaces and series Marcel Dekker, New York, 1981.
  • [15]. Maddox I.J. Elements of Functional Analysis Cambridge Univ. Press, Cambridge, 1970.
There are 15 citations in total.

Details

Primary Language English
Journal Section Natural Sciences
Authors

Nazlım Deniz Aral

Şükran Konca

Publication Date December 8, 2017
Submission Date June 22, 2017
Acceptance Date October 23, 2017
Published in Issue Year 2017Volume: 38 Supplement Issue 4

Cite

APA Aral, N. D., & Konca, Ş. (2017). On Some New Ideal Convergent Sequence Spaces of -Method of Summability. Cumhuriyet Science Journal, 38(4), 130-137. https://doi.org/10.17776/csj.363614
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