Research Article
Year 2017,
Volume: 38 Issue: 3, 557 - 562, 30.09.2017
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 .
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.
Year 2017,
Volume: 38 Issue: 3, 557 - 562, 30.09.2017
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.
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 | |
| Publication Date | September 30, 2017 |
| Submission Date | March 9, 2017 |
| Acceptance Date | May 17, 2017 |
| Published in Issue | Year 2017Volume: 38 Issue: 3 |
