<abstract><p>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.</p></abstract>
Many researchs have been studied on quaternions since Hamilton introduced them to the literature in 1843. In our paper, we gave split dual Jacobsthal (SDJ) and split dual Jacobsthal-Lucas (SDJL) quaternions over the algebra H(μ,n) with the basis {1; e1; e2; e3}, where μ,n ∈ Z. Binet like formulaes are obtained for these quaternions. Also, given Vajda identities for SDJ and SDJL quaternions.As a special case of Vajda identities, d'Ocagne's, Cassini's and Catalan's identities are represented.
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