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An Application On The Lucas Numbers And Infinite Toeplitz Matrices

Yıl 2017, , 557 - 562, 30.09.2017
https://doi.org/10.17776/csj.340510

Öz

In this paper, we firstly establish the regular matrix  by using Lucas numbers. Then, by
introducing the sequence space
 with the help of the matrix , we show that this space is a BK-space and isomorphic to the space . Also, we give some inclusion relations by examining the relationship
between the space
 and the spaces  ve  for .

Kaynakça

  • [1]. Koshy T., Fibonacci and Lucas Numbers with Applications. John Wiley & Sons, Inc., Canada, 2001.
  • [2]. Vajda S., Fibonacci and Lucas Numbers, and the Golden Section: Theory and Applications. Dover Publications, Inc., New York, 1989.
  • [3]. Kalman D., Mena R., The Fibonacci Numbers: Exposed. Mathematics Magazine, 76 (3) 161-187, 2003.
  • [4]. Başar F., Summability Theory and Its Applications. Bentham e-Books, İstanbul.
  • [5]. Choudary B., Nanda S., Functional Analysis with Applications. John Wiley & Sons, Inc., New Delhi, India, 272-273.
  • [6]. Kara EE., Some Topological and Geometrical Properties of New Banach Sequence Spaces. J. Inequal. Appl., 2013:38, 15pp., 2013.
  • [7]. Kara EE., Başarır M., An Application of Fibonacci Numbers into Infinite Toeplitz Matrices. Caspian Journal of Mathematics Sciences, 1 (1) 1-6, 2012.
  • [8]. Karakaş M., A New Regular Matrix Defined by Fibonacci Numbers and Its Applications. BEU Journal of Science, 4 (2) 205-210, 2015.
  • [9]. Başarır M., Başar F., Kara EE, On the Spaces of Fibonacci Null and Convergent Sequences. Arxiv, 1309-0150, in press.
  • [10]. Candan M., Kayaduman K., Almost Convergent Sequence Space Derived by Generalized Fibonacci Matrix and Fibonacci Core. British Journal of Mathematics & Computer Science, 7 (2) 150-167, 2015.
  • [11]. Alotaibi A., Mursaleen M., Alamri B., Mohiuddine SA, Compact Operators on Some Fibonacci Difference Sequence Spaces. J. Inequal. Appl., 2015:203, 8pp., 2015.
  • [12]. Debnath S., Saha S., Some Newly Defined Sequence Spaces Using Regular Matrix of Fibonacci Numbers. Afyon Kocatepe University Journal of Science & Engineering, 14 (1) 1-3, 2014.
  • [13]. Wilansky A., Summability through Functional Analysis. North Holland Mathematics Studies 85, Elseiver Science Publishers, New York, 1984.
  • [14]. Mursaleen M., Noman AK, On the Spaces of Convergent and Bounded Sequences. Thai J. Math., 8 (2) 311-329, 2010.

Lucas Sayıları ve Sonsuz Toeplitz Matrisleri Üzerine Bir Uygulama

Yıl 2017, , 557 - 562, 30.09.2017
https://doi.org/10.17776/csj.340510

Öz

Bu çalışmada öncelikle Lucas sayılarını kullanarak regüler  matrisi oluşturuldu. Daha sonra
bu matris yardımıyla
 dizi uzayı tanımlanarak, bu
uzayın bir BK-uzayı olduğu ve
 uzayı ile izomorf olduğu
gösterildi. Ayrıca,
 dizi uzayının  şartı altında  ve  uzaylarıyla ilişkisi incelenerek
bazı kapsama bağıntıları verildi.

Kaynakça

  • [1]. Koshy T., Fibonacci and Lucas Numbers with Applications. John Wiley & Sons, Inc., Canada, 2001.
  • [2]. Vajda S., Fibonacci and Lucas Numbers, and the Golden Section: Theory and Applications. Dover Publications, Inc., New York, 1989.
  • [3]. Kalman D., Mena R., The Fibonacci Numbers: Exposed. Mathematics Magazine, 76 (3) 161-187, 2003.
  • [4]. Başar F., Summability Theory and Its Applications. Bentham e-Books, İstanbul.
  • [5]. Choudary B., Nanda S., Functional Analysis with Applications. John Wiley & Sons, Inc., New Delhi, India, 272-273.
  • [6]. Kara EE., Some Topological and Geometrical Properties of New Banach Sequence Spaces. J. Inequal. Appl., 2013:38, 15pp., 2013.
  • [7]. Kara EE., Başarır M., An Application of Fibonacci Numbers into Infinite Toeplitz Matrices. Caspian Journal of Mathematics Sciences, 1 (1) 1-6, 2012.
  • [8]. Karakaş M., A New Regular Matrix Defined by Fibonacci Numbers and Its Applications. BEU Journal of Science, 4 (2) 205-210, 2015.
  • [9]. Başarır M., Başar F., Kara EE, On the Spaces of Fibonacci Null and Convergent Sequences. Arxiv, 1309-0150, in press.
  • [10]. Candan M., Kayaduman K., Almost Convergent Sequence Space Derived by Generalized Fibonacci Matrix and Fibonacci Core. British Journal of Mathematics & Computer Science, 7 (2) 150-167, 2015.
  • [11]. Alotaibi A., Mursaleen M., Alamri B., Mohiuddine SA, Compact Operators on Some Fibonacci Difference Sequence Spaces. J. Inequal. Appl., 2015:203, 8pp., 2015.
  • [12]. Debnath S., Saha S., Some Newly Defined Sequence Spaces Using Regular Matrix of Fibonacci Numbers. Afyon Kocatepe University Journal of Science & Engineering, 14 (1) 1-3, 2014.
  • [13]. Wilansky A., Summability through Functional Analysis. North Holland Mathematics Studies 85, Elseiver Science Publishers, New York, 1984.
  • [14]. Mursaleen M., Noman AK, On the Spaces of Convergent and Bounded Sequences. Thai J. Math., 8 (2) 311-329, 2010.
Toplam 14 adet kaynakça vardır.

Ayrıntılar

Bölüm Makaleler
Yazarlar

Murat Karakaş

Hasan Karabudak

Yayımlanma Tarihi 30 Eylül 2017
Gönderilme Tarihi 9 Mart 2017
Kabul Tarihi 17 Mayıs 2017
Yayımlandığı Sayı Yıl 2017

Kaynak Göster

APA Karakaş, M., & Karabudak, H. (2017). An Application On The Lucas Numbers And Infinite Toeplitz Matrices. Cumhuriyet Science Journal, 38(3), 557-562. https://doi.org/10.17776/csj.340510