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Öğe BEHAVIOR OF POSITIVE SOLUTIONS OF A DIFFERENCE EQUATION(KOREAN SOC COMPUTATIONAL & APPLIED MATHEMATICS & KOREAN SIGCAM, 2017) Tollu, D. T.; Yazlik, Y.; Taskara, N.In 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.Öğe The Construction of Horadam Numbers in Terms of the Determinant of Tridiagonal Matrices(AMER INST PHYSICS, 2011) Taskara, N.; Uslu, K.; Yazlik, Y.; Yilmaz, N.In this study, by using determinants of tridiagonal matrices, we mainly obtain Horadam numbers with positive and negative indices. Therefore we establish a new generalization for the tridiagonal matrices that represent well known numbers such as Fibonacci, Lucas, Jacobsthal, Jacobsthal-Lucas, Pell and Pell-Lucas numbers.Öğe The Generalized (s, t)-Sequence and its Matrix Sequence(AMER INST PHYSICS, 2011) Yazlik, Y.; Taskara, N.; Uslu, K.; Yilmaz, N.In this study, we first define a new sequence in which it generalizes (s, t)-Fibonacci and (s, t)-Lucas sequences at the same time. After that, by using it, we establish generalized (s, t)-matrix sequences. Finally we present some important relationships among this new generalization, (s, t)-Fibonacci and (s, t)-Lucas sequences and their matrix sequences.Öğe On fourteen solvable systems of difference equations(ELSEVIER SCIENCE INC, 2014) Tollu, D. T.; Yazlik, Y.; Taskara, N.In 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.Öğe On the Behaviour of Solutions for Some Systems of Difference Equations(EUDOXUS PRESS, LLC, 2015) Yazlik, Y.; Tollu, D. T.; Taskara, N.In this paper, we investigate the forms of the solutions of difference equation systems where the initial values are arbitrary nonzero real numbers such that the denominator is always nonzero. Also we deal with the behavior of the solutions of these systems.Öğe On the Behaviour of the Solutions of Difference Equation Systems(EUDOXUS PRESS, LLC, 2014) Yazlik, Y.; Elsayed, E. M.; Taskara, N.In 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.Öğe On the Binomial Sums of k-Fibonacci and k-Lucas sequences(AMER INST PHYSICS, 2011) Yilmaz, N.; Taskara, N.; Uslu, K.; Yazlik, Y.The main purpose of this paper is to establish some new properties of k-Fibonacci and k-Lucas numbers in terms of binomial sums. By that, we can obtain these special numbers in a new and direct way. Moreover, some connections between k-Fibonacci and k-Lucas numbers are revealed to get a more strong result.Öğe On the solutions of a max-type difference equation system(WILEY, 2015) Yazlik, Y.; Tollu, D. T.; Taskara, N.In 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.
