An Application On The Lucas Numbers And Infinite Toeplitz Matrices

Murat Karakaş; Hasan Karabudak

doi:10.17776/csj.340510

Research Article

An Application On The Lucas Numbers And Infinite Toeplitz Matrices

Year 2017, , 557 - 562, 30.09.2017

Murat Karakaş , Hasan Karabudak

https://doi.org/10.17776/csj.340510

Cited By: 6

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, , 557 - 562, 30.09.2017

Murat Karakaş , Hasan Karabudak

https://doi.org/10.17776/csj.340510

Cited By: 6

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 2017

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