A New Aspect of Dual Fibonacci Quaternions

On Dual-Hyperbolic Numbers with Generalized Fibonacci and Lucas Numbers Components

“…Equations 1) and 2) are found by taking the identity H n+1 + H n−1 = pL n + qL n−1 (see ref. [4]) and using the recurrence relation H n = (p − q)F n + qF n+1 , respectively. Here, if the values p = 1, q = 0 are specially taken in the generalized Fibonacci number H n , then the desired results are obtained.…”

Dual Pell Quaternions

“…In 2+016, Yüce and Torunbalc1 Ayd1n 6 defined dual Fibonacci quaternions as follows 6 : H D = {Q n = F n + i F n+1 + j F n+2 + k F n+3 | F n n-th Fibonacci number}, (1.5) where i 2 = j 2 = k 2 = i j k = 0 , i j = j i = j k = k j = k i = i k = 0. In 1971, Horadam studied on the Pell and Pell-Lucas sequences and he gave Cassini-like formula as follows 7 :…”

“…Several authors worked on different quaternions and their generalizations [12][13][14][15][16][17][18][19][20][21][22] . Also, some authors worked on dual quaternions and their generalizations [2][3][4][5][6] as follows:…”

Dual third-order Jacobsthal quaternions

“…where i 2 = j 2 = k 2 = ijk = −1 and F n is the n-th dual Fibonacci number. In 2016, Yüce and Torunbalcı Aydın [17] defined dual Fibonacci quaternions as follows:…”