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The matrix sequence in terms of bi-periodic fibonacci numbers
(ANKARA UNIV, FAC SCI, 2019) Coskun, Arzu.; Taskara, Necati.
In this paper, we define the bi-periodic Fibonacci matrix sequence that represent bi-periodic Fibonacci numbers. Then, we investigate generating function, Binet formula and summations of bi-periodic Fibonacci matrix sequence. After, we say that some behaviours of bi-periodic Fibonacci numbers can be obtained via the properties of this new matrix sequence. Finally, we express that well-known matrix sequences such as Fibonacci, Pell, k-Fibonacci matrix sequences are special cases of this generalized matrix sequence.
A solvable system of difference equations
(KOREAN MATHEMATICAL SOC, 2020) Taskara, Necati.; Tollu, Durhasan T.; Touafek, Nouressadat.; Yazlik, Yasin.
In this paper, we show that the system of difference equations x(n )= ay(n-1)(p )+ b(x(n-2)y(n-1))(p-1)/cy(n-1) + dx(n-2)(p-1), y(n) = alpha x(n-1)(p )+ beta(y(n-2)x(n-1))(p-1)/gamma x(n-1) + delta y(n-2)(p-1), n is an element of N-0 where the parameters a, b, c, d, alpha, beta, gamma, delta, p and the initial values x(-2) , x(-1), y(-2), y(-1) are real numbers, can be solved. Also, by using obtained formulas, we study the asymptotic behaviour of well-defined solutions of aforementioned system and describe the forbidden set of the initial values. Our obtained results significantly extend and develop some recent results in the literature.