38 research outputs found
Tribonacci and tribonacci-lucas numbers via the determinants of special matrices
No full textIn this paper, by using determinants of special matrices, it has been mainly obtained Tribonacci and Tribonacci-Lucas numbers. © 2014 Nazmiye Yilmaz and Necati Taskara
Generating matrix of the bi-periodic Lucas numbers
No full textInternational Conference on Numerical Analysis and Applied Mathematics (ICNAAM) -- SEP 19-25, 2016 -- Rhodes, GREECEIn this paper, firstly, we introduce the Q(l)-Generating matrix for the bi-periodic Lucas numbers. Then, by taking into account this matrix representation, we obtain some properties for the bi-periodic Fibonacci and Lucas numbers
BEHAVIOR OF POSITIVE SOLUTIONS OF A DIFFERENCE EQUATION
Get PDFIn this paper we deal with the difference equation y(n+1) -ay(n-1)/byny(n-1) +cy(n-1)y(n-2) +d, n is an element of N-0,N- where the coefficients a, b, c, d are positive real numbers and the initial conditions y-2, y-1, y-0 are nonnegative real numbers. Here, we investigate global asymptotic stability, periodicity, boundedness and oscillation of positive solutions of the above equation
On fourteen solvable systems of difference equations
Get PDFIn this paper, we mainly consider the systems of difference equations x(n+1) = 1+p(n)/q(n), y(n+1) = 1+r(n)/s(n), n is an element of N-0, where each of the sequences p(n); q(n); r(n) and s(n) represents either the sequence x(n) or the sequence y(n), with nonzero real initial values x(0) and y(0). Then we solve fourteen out of sixteen possible systems. It is noteworthy to depict that the solutions are presented in terms of Fibonacci numbers for twelve systems of these fourteen systems. (C) 2014 Elsevier Inc. All rights reserved
On the solutions of a max‐type difference equation system
Get PDFIn this paper, we study behavior of the solution of the following max-type difference equation system: x(n+1) = max {1/x(n), min {1,A/y(n)}}, y(n+1) = max {1/y(n), min {1,A/x(n)}}, n is an element of N-0, where N-0 = N boolean OR {0} , the parameter A is positive real number, and the initial values x(0,) y(0) are positive real numbers. Copyright (C) 2015 John Wiley & Sons, Ltd
On the Behaviour of the Solutions of Difference Equation Systems
No full textIn this paper, we investigate the behaviour of the solutions of difference equations systems x(n+1) = y(n-5)/+/- 1 + y(n-1)x(n-3)y(n-5), y(n+1) = x(n-5)/+/- 1 + x(n-1)y(n-3)x(n-5), where the initial values are arbitrary real numbers such that the denominator is always nonzero.King Abdulaziz University, Jeddah; DSRThis article was funded by the Deanship of Scientific Research (DSR), King Abdulaziz University, Jeddah. The authors, therefore, acknowledge with thanks DSR technical and financial support
The Generalized k-Fibonacci and k-Lucas Numbers
No full textIn this paper we give the generalization {G(k,n)}(n is an element of N) of k-Fibonacci and k-Lucas numbers. After that, by using this generalization, it has been obtained some new algebraic properties on these numbers
The periodicity and solutions of the rational difference equation with periodic coefficients
No full textAbstractIn this paper, we give necessary and sufficient conditions for generalized solution and periodicity of the difference equation xn+1=pnxn−k+xn−(k+1)qn+xn−(k+1) with (k+2)-periodic coefficients, where k∈N, x−k−1,x−k,⋯,x0∈R. Also, we obtain that the generalized solution is periodic with (k+1)-period
A note on generalized k-Horadam sequence
No full textAbstractIn this paper, we define generalized k-Horadam sequence {Hk,n}n∈N. After that, we study the properties of the generalized k-Horadam sequence and prove some of these properties by means of determinant. Also, we obtain a generating function for the generalized k-Horadam sequence
