On Dual Quaternions with k−Generalized Leonardo Components

YILMAZ, ÇİĞDEM ZEYNEP; Saçlı, Gülsüm Yeliz

doi:10.53570/jnt.1328605

On Dual Quaternions with k−Generalized Leonardo Components

Çiğdem Zeynep YILMAZ, (Yıldız Teknik Üniversitesi, Fen-Edebiyat Fakültesi, Matematik Bölümü, İstanbul, Türkiye)

Gülsüm Yeliz SAÇLI (Yıldız Teknik Üniversitesi, Fen-Edebiyat Fakültesi, Matematik Bölümü, İstanbul, Türkiye)

Journal of New Theory

7 1

Yıl: 2023 Cilt: Sayı: 44 Sayfa Aralığı: 31 - 42 Metin Dili: İngilizce DOI: 10.53570/jnt.1328605 İndeks Tarihi: 22-10-2023

On Dual Quaternions with k−Generalized Leonardo Components

Öz:

In this paper, we define a one-parameter generalization of Leonardo dual quaternions, namely $k-$generalized Leonardo-like dual quaternions. We introduce the properties of $k$-generalized Leonardo-like dual quaternions, including relations with Leonardo, Fibonacci, and Lucas dual quaternions. We investigate their characteristic relations, involving the Binet-like formula, the generating function, the summation formula, Catalan-like, Cassini-like, d'Ocagne-like, Tagiuri-like, and Hornsberger-like identities. The crucial part of the present paper is that one can reduce the calculations of Leonardo-like dual quaternions by considering $k$. For $k=1$, these results are generalizations of the ones for ordered Leonardo quadruple numbers. Finally, we discuss the need for further research.

Anahtar Kelime: Leonardo sequence recurrence relations dual quaternions

Belge Türü: Makale Makale Türü: Araştırma Makalesi Erişim Türü: Erişime Açık

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APA	YILMAZ Ç, Saçlı G (2023). On Dual Quaternions with k−Generalized Leonardo Components. , 31 - 42. 10.53570/jnt.1328605
Chicago	YILMAZ ÇİĞDEM ZEYNEP,Saçlı Gülsüm Yeliz On Dual Quaternions with k−Generalized Leonardo Components. (2023): 31 - 42. 10.53570/jnt.1328605
MLA	YILMAZ ÇİĞDEM ZEYNEP,Saçlı Gülsüm Yeliz On Dual Quaternions with k−Generalized Leonardo Components. , 2023, ss.31 - 42. 10.53570/jnt.1328605
AMA	YILMAZ Ç,Saçlı G On Dual Quaternions with k−Generalized Leonardo Components. . 2023; 31 - 42. 10.53570/jnt.1328605
Vancouver	YILMAZ Ç,Saçlı G On Dual Quaternions with k−Generalized Leonardo Components. . 2023; 31 - 42. 10.53570/jnt.1328605
IEEE	YILMAZ Ç,Saçlı G "On Dual Quaternions with k−Generalized Leonardo Components." , ss.31 - 42, 2023. 10.53570/jnt.1328605
ISNAD	YILMAZ, ÇİĞDEM ZEYNEP - Saçlı, Gülsüm Yeliz. "On Dual Quaternions with k−Generalized Leonardo Components". (2023), 31-42. https://doi.org/10.53570/jnt.1328605

APA	YILMAZ Ç, Saçlı G (2023). On Dual Quaternions with k−Generalized Leonardo Components. Journal of New Theory, (44), 31 - 42. 10.53570/jnt.1328605
Chicago	YILMAZ ÇİĞDEM ZEYNEP,Saçlı Gülsüm Yeliz On Dual Quaternions with k−Generalized Leonardo Components. Journal of New Theory , no.44 (2023): 31 - 42. 10.53570/jnt.1328605
MLA	YILMAZ ÇİĞDEM ZEYNEP,Saçlı Gülsüm Yeliz On Dual Quaternions with k−Generalized Leonardo Components. Journal of New Theory, vol., no.44, 2023, ss.31 - 42. 10.53570/jnt.1328605
AMA	YILMAZ Ç,Saçlı G On Dual Quaternions with k−Generalized Leonardo Components. Journal of New Theory. 2023; (44): 31 - 42. 10.53570/jnt.1328605
Vancouver	YILMAZ Ç,Saçlı G On Dual Quaternions with k−Generalized Leonardo Components. Journal of New Theory. 2023; (44): 31 - 42. 10.53570/jnt.1328605
IEEE	YILMAZ Ç,Saçlı G "On Dual Quaternions with k−Generalized Leonardo Components." Journal of New Theory, , ss.31 - 42, 2023. 10.53570/jnt.1328605
ISNAD	YILMAZ, ÇİĞDEM ZEYNEP - Saçlı, Gülsüm Yeliz. "On Dual Quaternions with k−Generalized Leonardo Components". Journal of New Theory 44 (2023), 31-42. https://doi.org/10.53570/jnt.1328605