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Yüksel Soykan

Publications and source records attributed to Yüksel Soykan.

13 recordsLinked to original sources
arXiv2021

Global Dynamical Behaviours and Periodicity of a Certain Quadratic-Rational Difference Equation with Delay

Our aim in this paper is to deal with the dynamics of following higher order difference equation x_{n+1}=A+B((x_{n-m})/(x_{n}^2)) where A,B>0, and initial values are positive, and m={1,2,...}. Furthermore, we discuss the periodicity, boundedness, semi-cycles, global asymptotic stability of solutions of these equations. We also handle the rate of convergence of solutions of these difference equations.

math.DS↗
arXiv2019

Summing Formulas For Generalized Tribonacci Numbers

In this paper, closed forms of the summation formulas for generalized Tribonacci numbers are presented. Then, some previous results are recovered as particular cases of the present results. As special cases, we give summation formulas of Tribonacci, Tribonacci-Lucas, Padovan, Perrin, Narayana and some other third order linear recurrance sequences. All the summing formulas of well known recurrence sequences which we deal with are linear except the cases Pell-Padovan and Padovan-Perrin.

math.GM↗
arXiv2019

On the Solutions of Systems of Difference Equations via Tribonacci Numbers

The main objective of this paper is to investigate the explicit form, stability character and global behavior of solutions of the following two systems of rational difference equations x_{n+1}=((+(-)1)/(y_{n}(x_{n-1}+(-)1)+1)), y_{n+1}=((+(-)1)/(x_{n}(y_{n-1}+(-)1)+1)), n=0,1,... such that their solutions are associated with Tribonacci numbers.

math.DS↗
arXiv2019

Simson Identity of Generalized m-step Fibonacci Numbers

One of the best known and oldest identities for the Fibonacci sequence $F_n$ is $F_{n+1}F_{n-1}-F_{n}^2=(-1)^n$ which was derived first by R. Simson in 1753 and it is now called as Simson or Cassini Identity. In this paper, we generalize this result to generalized m-step Fibonacci numbers and give an attractive formula. Furthermore, we present some Simson's identities of particular generalized m-step Fibonacci sequences.

math.NT↗
arXiv2019

Tetranacci and Tetranacci-Lucas Quaternions

The quaternions form a 4-dimensional Cayley-Dickson algebra. In this paper, we introduce the Tetranacci and Tetranacci-Lucas quaternions. Furthermore, we present some properties of these quaternions and derive relationships between them.

math.RA↗
arXiv2019

Gaussian Generalized Tetranacci Numbers

In this paper, we define Gaussian generalized Tetranacci numbers and as special cases, we investigate Gaussian Tetranacci and Gaussian Tetranacci-Lucas numbers with their properties.

math.NT↗
arXiv2019

On Generalized Tribonacci Sedenions

The sedenions form a 16-dimensional Cayley-Dickson algebra. In this work, we introduce the generalized Tribonacci sedenion and present some properties of this sedenion.

math.RA↗
arXiv2018

On the Dynamics of a Higher Order Nonlinear System of Difference Equations

The aim of this paper is to investigate the dynamics of a higher order system of rational difference equations. Our concentration is on boundedness character, the oscillatory, the existence of unbounded solutions and the global behavior of positive solutions for the following system of difference equations \begin{equation*} x_{n+1}=A+\frac{x_{n-m}}{z_{n}},\ y_{n+1}=A+\frac{y_{n-m}}{z_{n}},\ z_{n+1}=A+\frac{z_{n-m}}{y_{n}},\ n=0,1,...,\end{equation*} where $A$ and the initial values $x_{-i}$, $y_{-i}$, $z_{-i}$, for $i=0,1,...,m$, are positive real numbers.

math.DS↗
arXiv2018

Tribonacci and Tribonacci-Lucas Sedenions

The sedenions form a 16-dimensional Cayley-Dickson algebra. In this paper, we introduce the Tribonacci and Tribonacci-Lucas sedenions. Furthermore, we present some properties of these sedenions and derive relationships between them.

math.RA↗