Open AccessSome properties and Vajda theorems of split dual Fibonacci and split dual Lucas octonions
Author(s) -
Ümit Tokeşer,
Tuğba Mert,
Yakup Dündar
Publication year - 2022
Publication title -
aims mathematics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.329
H-Index - 15
ISSN - 2473-6988
DOI - 10.3934/math.2022483
Subject(s) - fibonacci number , lucas number , dual (grammatical number) , identity (music) , mathematics , catalan number , combinatorics , lucas sequence , fibonacci polynomials , pure mathematics , algebra over a field , discrete mathematics , physics , philosophy , linguistics , acoustics , orthogonal polynomials , difference polynomials
In this paper, we introduce split dual Fibonacci and split dual Lucas octonions over the algebra $ \widetilde{\widetilde{O}}\left(a, b, c\right) $, where $ a, b $ and $ c $ are real numbers. We obtain Binet formulas for these octonions. Also, we give many identities and Vajda theorems for split dual Fibonacci and split dual Lucas octonions including Catalan's identity, Cassini's identity and d'Ocagne's identity.