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An Application On The Lucas Numbers And Infinite Toeplitz Matrices

Year 2017, Volume: 38 Issue: 3, 557 - 562, 30.09.2017

Murat Karakaş Hasan Karabudak

https://doi.org/10.17776/csj.340510
Cited By: 3

Abstract

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 .

Keywords

Lucas numbers Regular matrix Fibonacci numbers Sequence space

References

  • [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

Year 2017, Volume: 38 Issue: 3, 557 - 562, 30.09.2017

Murat Karakaş Hasan Karabudak

https://doi.org/10.17776/csj.340510
Cited By: 3

Abstract

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.

Keywords

Lucas sayıları Regüler matris Fibonacci sayıları Dizi uzayı

References

  • [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.
There are 14 citations in total.

Details

Journal Section Articles
Authors

Murat Karakaş

Hasan Karabudak

Publication Date September 30, 2017
Submission Date March 9, 2017
Acceptance Date May 17, 2017
Published in Issue Year 2017Volume: 38 Issue: 3

Cite

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

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https://doi.org/10.33434/cams.1414791
A New Outlook for Almost Convergent Sequence Spaces
Cumhuriyet Science Journal
https://doi.org/10.17776/csj.383311
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