Journals / Journal of New Results in Science / 2021 / Cilt: 10 - Sayı: 3

On some identities and Hankel matrices norms involving new defined generalized modified pell numbers

Pages
60–66
Publication Date
2021-12-31
DOI
—
🏛️Bibliographic metadata and full text access for this article are provided via DergiPark.
DergiPark Record ↗
✨

AI Summary & Key Takeaways

AI Insight
⚡ TL;DR(Too Long; Didn't Read)

Finally, using these sequences the row and column norms of the Hankel matrices are presented.

📌 3 Key Takeaways

🎯
Objective & Hypothesis:The aim of this paper is to introduce a generalization of Modified Pell numbers.
📊
Key Findings & Data:Some identities about this new sequence are obtained and also investigated some relationships with another sequence.
💡
Conclusion & Impact:Finally, using these sequences the row and column norms of the Hankel matrices are presented.
🔬Design:Research Article
📍Scope:Comprehensive Sample
⚙️Variables:Modified Pell Numbers · Hankel Matrices · Matrix Norms

Abstract

The aim of this paper is to introduce a generalization of Modified Pell numbers. Some identities about this new sequence are obtained and also investigated some relationships with another sequence. Finally, using these sequences the row and column norms of the Hankel matrices are presented.

🔖

Cite This Article

KIZILIRMAK, G. Ö. (2021). On some identities and Hankel matrices norms involving new defined generalized modified pell numbers. Journal of New Results in Science, Cilt: 10 - Sayı: 3, 60–66. https://ajindex.com/articles/777790

📄 Full Text PDF Viewer

📄

PDF görüntüleyici hazırlanıyor...

References (11)

  1. A. F. Horadam, Jacobsthal representation numbers, Fibonacci Quarterly, 34, (1996) 40–54.
  2. T. Koshy, Fibonacci and Lucas numbers with applications, John Wiley and Sons Inc., New York, 2001.
  3. G. K. Panda, Sequence balancing and cobalancing numbers, Fibonacci Quarterly, 45, (2007) 265–271.
  4. A. F. Horadam, Pell identities, Fibonacci Quarterly, 9, (1971) 245–252.
  5. S. Halici, On some inequality and Hankel matrices involving Pell, Pell Lucas numbers, Mathematical Reports, 15, (2013) 1–10.
  6. G. Bilgici, New generalizations of Fibonacci and Lucas numbers, Applied Mathematical Sciences, 8, (2014) 1429–1437.
  7. S. Falcon, A. Plaza, On the Fibonacci k-numbers, Chaos Solitions and Fractals, 32, (2007) 1615–1624. A. Szynal-Liana,, A. Wloch, I. Wloch, On generalized Pell numbers generated by Fibonacci and Lucas numbers, Ars Combinatoria, 115, (2014) 411–423.
  8. D. Tasci, E. Sevgi, Bi-periodic balancing numbers, Journal of Science and Arts, 50, (2020) 75–84.
  9. O.M. Yayenie, A. Edson, New generalization of Fibonacci sequences and extended Binet’s formula, Integers, 9, (2009) 639–654.
  10. L. Trojnar-Spelina, I. Wloch, On generalized Pell and Pell Lucas numbers, Iranian Journal of Science and Technology, Transactions A: Science, 43, (2019) 2871–2877.
  11. P. Vasco, P. Catarino, H. Campos„ A. P. Aires, A. Borges, k-Pell, k-Pell-Lucas and modified k-Pell Numbers: Some identities and norms of Hankel matrices, International Journal of Mathematical Analysis, 9,(2015) 31-37.