Investigation of Dual-Complex Fibonacci, Dual-Complex Lucas Numbers and Their Properties

Dual-complex generalized k-Horadam numbers

“…This study aims to generalize several dual complex numbers in the literature such as [1,10]. Also, we obtain numerous new dual complex numbers for the special cases of f (k); g(k); a and b (see Table 2).…”

“…In the 19 th century, Cli¤ord described the dual numbers with in the form A = a+"a , where a; a 2 R, " 2 = 0 and " 6 = 0 [4]. Up to this time, there are number of studies in the literature that concern about the dual numbers and dual complex numbers [1,3,5,[8][9][10][17][18][19][20]. For instance, Fjelstad and Gal examined the extensions of the hyperbolic complex numbers to n dimensions and they presented n dimensional dual complex numbers [9].…”

“…Up until now, some researchers have studied dual complex numbers with Fibonacci and Lucas numbers. For example, Güngör and Azak de…ned dual complex Fibonacci and Lucas numbers and investigate some properties of these numbers such as Binet formulas, Cassini and Catalan identities [10]. Ayd¬n, presented dual complex k Fibonacci numbers and then examine some algebraic properties of dual complex k Fibonacci numbers which are related to dual complex numbers and k Fibonacci numbers [1].…”

“…Inspiring by these studies and by combining dual complex numbers and generalized k Horadam numbers, in this paper, we de…ne the dual complex generalized k Horadam numbers which is a generalization of the studies [10], [1] as presented in Table 2. The next section describes the dual complex generalized k Horadam numbers and contains various theorems and corollaries regarding the dual complex generalized k Horadam numbers.…”

Dual-complex k-Pell quaternions

“…There are many applications for the theory of dual-complex numbers. In 2017, Güngör and Azak defined dual-complex Fibonacci and dualcomplex Lucas numbers and their properties [12].…”