Mλ- Toplanabilme Metoduyla Tanımlanan Bazı Yeni İdeal Yakınsak Dizi Uzayları

Yıl 2017, Cilt: 38 Ek Sayı 4, 130 - 137, 08.12.2017

Nazlım Deniz Aral Şükran Konca

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

Öz

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.

Anahtar Kelimeler

-yakınsaklık, Orlicz fonksiyonu, -toplanabilme metodu, dizi uzayı

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

Öz

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.

Anahtar Kelimeler

-convergence, Orlicz function, -method of summability, sequence space

Kaynakça

• [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.