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Yıl 2020, Cilt: 8 Sayı: 1, 79 - 90, 15.04.2020

İnci Okumuş Yüksel Soykan

Öz

Kaynakça

  • [1] A. M. Alotaibi, M. S. M. Noorani and M. A. El-Moneam, On the Solutions of a System of Third-Order Rational Difference Equations, Discrete Dynamics in Nature and Society, Article ID 1743540, 11 pages (2018).
  • [2] D. T. Tollu, Y. Yazlık and N. Taskara, On the solutions of two special types of Riccati difference equation via Fibonacci numbers, Advances in Difference Equations, 2013:174 (2013).
  • [3] D. T. Tollu, Y. Yazlık and N. Taskara, The Solutions of Four Riccati Difference Equations Associated with Fibonacci numbers, Balkan Journal of Mathematics, 2: 163-172 (2014).
  • [4] D. T. Tollu, Y. Yazlık and N. Taskara, On fourteen solvable systems of difference equations, Applied Mathematics and Computation, 233: 310-319 (2014).
  • [5] J.B. Bacani and J. F. T. Rabago, On Two Nonlinear Difference Equations, Dynamics of Continuous, Discrete and Impulsive Systems, (Serias A) to appear (2015).
  • [6] J. F. T. Rabago, On the Closed-Form Solution of a Nonlinear Difference Equation and Another Proof to Sroysang’s Conjecture, arXiv:1604.06659v1 [math.NT] (2016).
  • [7] M. M. El-Dessoky, On the dynamics of higher order difference equations $x_{n+1}=ax_{n}+\frac{\alpha x_{n}x_{n-l}}{\beta x_{n}+\gamma x_{n-k}}$, J. Computational Analysis and Applications, 22(7): 1309-1322 (2017).
  • [8] M. M. El-Dessoky, E. M. Elabbasy and A. Asiri, Dynamics and Solutions of a Fifth-Order Nonlinear Difference Equations. Discrete Dynamics in Nature and Society, Article ID 9129354, 21 pages (2018).
  • [9] O. Ocalan and O. Duman, On Solutions of the Recursive Equations$x_{n+1}=x_{n-1}^{p}/x_{n}^{p}$ ($p>0$) via Fibonacci-Type Sequences, Electronic Journal of Mathematical Analysis and Applications, 7(1): 102-115 (2019).
  • [10] S. Stevic, B. Iricanin, W. Kosmala and Z. Smarda, Representation of solutions of a solvable nonlinear difference equation of second order, Electronic Journal of Qualitative Theory of Differential Equations, 95: 1-18 (2018).
  • [11] Y. Akrour, N. Touafek and Y. Halim, On a System of Difference Equations of Second Order Solved in a Closed Form, arXiv:1904.04476v1, [math.DS] (2019).
  • [12] Y. Halim, Global Character of Systems of Rational Difference Equations, Electronic Journal of Mathematical Analysis and Applications, 3(1): 204-214 (2015).
  • [13] Y. Halim and M. Bayram, On the solutions of a higher-order difference equation in terms of generalized Fibonacci sequences, Mathematical Methods in the Applied Sciences, 39: 2974-2982 (2016).
  • [14] Y. Halim, A System of Difference Equations with Solutions Associated to Fibonacci Numbers, International Journal of Difference Equations, 11(1): 65-77 (2016).
  • [15] Y. Halim and J. F. T. Rabago, On Some Solvable Systems of Difference Equations with Solutions Associated to Fibonacci Numbers, Electronic Journal of Mathematical Analysis and Applications, 5(1): 166-178 (2017).
  • [16] Y. Halim and J. F. T. Rabago, On the Solutions of a Second-Order Difference Equation in terms of Generalized Padovan Sequences, Mathematica Slovaca, 68(3): 625-638 (2018).
  • [17] Y. Yazlık, D. T. Tollu and N. Tas¸kara On the Solutions of Difference Equation Systems with Padovan Numbers. Applied Mathematics, 4:15-20 (2013).

On the Solutions of Four Rational Difference Equations Associated to Tribonacci Numbers

Yıl 2020, Cilt: 8 Sayı: 1, 79 - 90, 15.04.2020

İnci Okumuş Yüksel Soykan

Öz

In this study, we investigate the form of solutions, stability character and asymptotic behavior of the following four rational difference equations% \begin{eqnarray*} x_{n+1} &=&\frac{1}{x_{n}\left( x_{n-1}\pm 1\right) \pm 1}\text{,} \\ x_{n+1} &=&\frac{-1}{x_{n}\left( x_{n-1}\pm 1\right) \mp 1}\text{,} \end{eqnarray*}% such that their solutions are associated with Tribonacci numbers.

Anahtar Kelimeler

difference equations; equilibrium point; global asymptotic stability; solutions; tribonacci number

Kaynakça

  • [1] A. M. Alotaibi, M. S. M. Noorani and M. A. El-Moneam, On the Solutions of a System of Third-Order Rational Difference Equations, Discrete Dynamics in Nature and Society, Article ID 1743540, 11 pages (2018).
  • [2] D. T. Tollu, Y. Yazlık and N. Taskara, On the solutions of two special types of Riccati difference equation via Fibonacci numbers, Advances in Difference Equations, 2013:174 (2013).
  • [3] D. T. Tollu, Y. Yazlık and N. Taskara, The Solutions of Four Riccati Difference Equations Associated with Fibonacci numbers, Balkan Journal of Mathematics, 2: 163-172 (2014).
  • [4] D. T. Tollu, Y. Yazlık and N. Taskara, On fourteen solvable systems of difference equations, Applied Mathematics and Computation, 233: 310-319 (2014).
  • [5] J.B. Bacani and J. F. T. Rabago, On Two Nonlinear Difference Equations, Dynamics of Continuous, Discrete and Impulsive Systems, (Serias A) to appear (2015).
  • [6] J. F. T. Rabago, On the Closed-Form Solution of a Nonlinear Difference Equation and Another Proof to Sroysang’s Conjecture, arXiv:1604.06659v1 [math.NT] (2016).
  • [7] M. M. El-Dessoky, On the dynamics of higher order difference equations $x_{n+1}=ax_{n}+\frac{\alpha x_{n}x_{n-l}}{\beta x_{n}+\gamma x_{n-k}}$, J. Computational Analysis and Applications, 22(7): 1309-1322 (2017).
  • [8] M. M. El-Dessoky, E. M. Elabbasy and A. Asiri, Dynamics and Solutions of a Fifth-Order Nonlinear Difference Equations. Discrete Dynamics in Nature and Society, Article ID 9129354, 21 pages (2018).
  • [9] O. Ocalan and O. Duman, On Solutions of the Recursive Equations$x_{n+1}=x_{n-1}^{p}/x_{n}^{p}$ ($p>0$) via Fibonacci-Type Sequences, Electronic Journal of Mathematical Analysis and Applications, 7(1): 102-115 (2019).
  • [10] S. Stevic, B. Iricanin, W. Kosmala and Z. Smarda, Representation of solutions of a solvable nonlinear difference equation of second order, Electronic Journal of Qualitative Theory of Differential Equations, 95: 1-18 (2018).
  • [11] Y. Akrour, N. Touafek and Y. Halim, On a System of Difference Equations of Second Order Solved in a Closed Form, arXiv:1904.04476v1, [math.DS] (2019).
  • [12] Y. Halim, Global Character of Systems of Rational Difference Equations, Electronic Journal of Mathematical Analysis and Applications, 3(1): 204-214 (2015).
  • [13] Y. Halim and M. Bayram, On the solutions of a higher-order difference equation in terms of generalized Fibonacci sequences, Mathematical Methods in the Applied Sciences, 39: 2974-2982 (2016).
  • [14] Y. Halim, A System of Difference Equations with Solutions Associated to Fibonacci Numbers, International Journal of Difference Equations, 11(1): 65-77 (2016).
  • [15] Y. Halim and J. F. T. Rabago, On Some Solvable Systems of Difference Equations with Solutions Associated to Fibonacci Numbers, Electronic Journal of Mathematical Analysis and Applications, 5(1): 166-178 (2017).
  • [16] Y. Halim and J. F. T. Rabago, On the Solutions of a Second-Order Difference Equation in terms of Generalized Padovan Sequences, Mathematica Slovaca, 68(3): 625-638 (2018).
  • [17] Y. Yazlık, D. T. Tollu and N. Tas¸kara On the Solutions of Difference Equation Systems with Padovan Numbers. Applied Mathematics, 4:15-20 (2013).
Toplam 17 adet kaynakça vardır.

Ayrıntılar

Birincil Dil İngilizce
Konular Mühendislik
Bölüm Articles
Yazarlar

İnci Okumuş 0000-0003-3711-8144

Yüksel Soykan 0000-0002-1895-211X

Yayımlanma Tarihi 15 Nisan 2020
Gönderilme Tarihi 28 Haziran 2019
Kabul Tarihi 25 Şubat 2020
Yayımlandığı Sayı Yıl 2020 Cilt: 8 Sayı: 1

Kaynak Göster

APA Okumuş, İ., & Soykan, Y. (2020). On the Solutions of Four Rational Difference Equations Associated to Tribonacci Numbers. Konuralp Journal of Mathematics, 8(1), 79-90.
AMA Okumuş İ, Soykan Y. On the Solutions of Four Rational Difference Equations Associated to Tribonacci Numbers. Konuralp J. Math. Nisan 2020;8(1):79-90.
Chicago Okumuş, İnci, ve Yüksel Soykan. “On the Solutions of Four Rational Difference Equations Associated to Tribonacci Numbers”. Konuralp Journal of Mathematics 8, sy. 1 (Nisan 2020): 79-90.
EndNote Okumuş İ, Soykan Y (01 Nisan 2020) On the Solutions of Four Rational Difference Equations Associated to Tribonacci Numbers. Konuralp Journal of Mathematics 8 1 79–90.
IEEE İ. Okumuş ve Y. Soykan, “On the Solutions of Four Rational Difference Equations Associated to Tribonacci Numbers”, Konuralp J. Math., c. 8, sy. 1, ss. 79–90, 2020.
ISNAD Okumuş, İnci - Soykan, Yüksel. “On the Solutions of Four Rational Difference Equations Associated to Tribonacci Numbers”. Konuralp Journal of Mathematics 8/1 (Nisan 2020), 79-90.
JAMA Okumuş İ, Soykan Y. On the Solutions of Four Rational Difference Equations Associated to Tribonacci Numbers. Konuralp J. Math. 2020;8:79–90.
MLA Okumuş, İnci ve Yüksel Soykan. “On the Solutions of Four Rational Difference Equations Associated to Tribonacci Numbers”. Konuralp Journal of Mathematics, c. 8, sy. 1, 2020, ss. 79-90.
Vancouver Okumuş İ, Soykan Y. On the Solutions of Four Rational Difference Equations Associated to Tribonacci Numbers. Konuralp J. Math. 2020;8(1):79-90.
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