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Öğe The generalized bi-periodic fibonacci quaternions and octonions(Institute of Mathematics, 2019) Sahin M.; Tan E.; Yilmaz S.In this paper, we present a further generalization of the bi-periodic Fibonacci quaternions and octonions. We give the generating function, the Binet formula, and some basic properties of these quaternions and octonions. The results of this paper not only give a generalization of the bi-periodic Fibonacci quaternions and octonions, but also include new results such as the matrix representation and the norm value of the generalized bi-periodic Fibonacci sequence. © 2019 Novi Sad Journal of Mathematics. All rights reserved.