Dual third-order Jacobsthal quaternions.
ResumenIn 2016, Yüce and Torunbalcı Aydın (18) defined dual Fibonacci quaternions. In this paper, we defined the dual third-order Jacobsthal quaternions and dual third-order Jacobsthal-Lucas quaternions. Also, we investigated the relations between the dual third-order Jacobsthal quaternions and third-order Jacobsthal numbers. Furthermore, we gave some their quadratic properties, the summations, the Binet’s formulas and Cassini-like identities for these quaternions.
E. Ata and Y. Yaylı, Dual quaternions and dual projective spaces, Chaos, Solitons and Fractals, 40(3), pp. 1255-1263, (2009).
P. Barry, Triangle geometry and Jacobsthal numbers, Irish Math. Soc. Bull. 51, pp. 45-57, (2003).
G. Cerda-Morales, Identities for third order Jacobsthal quaternions, Advances in Applied Clifford Algebras 27 (2), pp. 1043-1053, (2017).
Ch. K. Cook and M. R. Bacon, Some identities for Jacobsthal and Jacobsthal-Lucas numbers satisfying higher order recurrence relations, Annales Mathematicae et Informaticae 41, pp. 27-39, (2013).
Z. Ercan and S. Yüce, On properties of the dual quaternions, Eur. J. Pure Appl. Math. 4 (2), pp. 142-146, (2011).
S. Halıcı, On Fibonacci quaternions, Advances in Applied Clifford Algebras 22(2), pp. 321-327, (2012).
C. J. Harman, Complex Fibonacci numbers, The Fibonacci Quarterly. 19 (1), pp. 82-86, (1981).
A. F. Horadam, A generalized Fibonacci sequence, The American Mathematical Monthly. 68 (5), pp. 455-459, (1961).
A. F. Horadam, Complex Fibonacci numbers and Fibonacci quaternions, American Math. Monthly. 70 (3), pp. 289-291, (1963).
A. F. Horadam , Quaternion recurrence relations, Ulam Quarterly. 2 (2), pp. 23-33, (1993).
A. F. Horadam , Jacobsthal representation numbers, Fibonacci Quarterly 34, pp. 40-54, (1996).
A. L. Iakin, Generalized quaternions of higher order, The Fibonacci Quarterly . 15 (4), pp. 343-346, (1977).
A. L. Iakin , Generalized quaternions with quaternion components, The Fibonacci Quarterly . 15 (4), pp. 350-352, (1977).
M. R. Iyer, A note on Fibonacci quaternions, The Fibonacci Quarterly . 7 (3), pp. 225-229, (1969).
M. R. Iyer , Some results on Fibonacci quaternions, The Fibonacci Quarterly . 7 (3), pp. 201-210, (1969).
V. Majernik, Quaternion formulation of the Galilean space-time transformation, Acta Phy. Slovaca., 56 (1), pp. 9-14, (2006).
K. S. Nurkan and I. A. Güven, Dual Fibonacci quaternions. Adv. Appl. Clifford Algebras. 25 (2), pp. 403-414, (2015).
S. Yüce and F. Torunbalcı Aydın, A new aspect of dual Fibonacci quaternions, Adv. Appl. Clifford Algebras. 26 (2), pp. 873-884, (2016).
S. Yüce and F. Torunbalcı Aydın, Generalized dual Fibonacci quaternions, Applied Mathematics E-Notes 16, pp. 276-289, (2016).