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Year 2021, Volume: 9 Issue: 2, 316 - 323, 15.10.2021

Ramazan Karataş Ali Gelişken

Abstract

References

  • A. Gelişken, On a system of rational difference equation, J. Computational Analysis and Applications, 23(4) (2017), 593-606.
  • D. Simsek, F. Abdullayev, On the recursive sequence x_{n+1}=((x_{n-(4k+3)})/(1+∏_{t=0}²x_{n-(k+1)t-k})), Journal of Mathematical Sciences, 6(222) (2017), 762-771.
  • D. Simsek, F. Abdullayev, On the recursive sequence x_{n+1}=((x_{n-(k+1)})/(1+x_{n}x_{n-1}...x_{n-k})), Journal of Mathematical Sciences, 234(1) (2018), 73-81.
  • E. M. Elsayed, F. Alzahrani, H. S. Alayachi, Formulas and properties of some class of nonlinear difference equation, J. Computational Analysis and Applications, 24(8) (2018),1517-1531.
  • M. B. Almatrafi, E. M. Elsayed, F. Alzahrani, Investigating some properties of a fourth order difference equation, J. Computational Analysis and Applications, 28(2) (2020), 243-253.
  • R. Abo-Zeid, Behavior of solutions of higher order difference equation, Alabama Journal of Mathematics, 42(2018), 1-10.
  • R. Karatas, Global behavior of a higher order difference equation, Computers and Mathematics with Applications, 60(2010), 830-839.
  • R. Karatas, On the solutions of the recursive sequence x_{n+1}=((αx_{n-(2k+1)})/(-a+x_{n-k}x_{n-(2k+1)})), Fasciculi Mathematici, 45(2010), 37-45.
  • S. Ergin, R. Karatas, On the solutions of the recursive sequence x_{n+1}=((αx_{n-k})/(a-∏_{i=0}^{k}x_{n-i})), Thai Journal of Mathematics, 14(2) (2016), 391-397.
  • V. L. Kocic, G. Ladas, Global Behavior of Nonlinear Difference Equations of High Order with Applications, Kluwer Academic Publishers, Dordrecht, 1993.

A Solution Form of A Higher Order Difference Equation

Year 2021, Volume: 9 Issue: 2, 316 - 323, 15.10.2021

Ramazan Karataş Ali Gelişken

Abstract

The main aim of this paper is to investigate the solutions of the difference equation \[ x_{n+1}=\frac{(-1)^{n}ax_{n-2k}}{a+(-1)^{n}\prod\limits_{i=0}^{2k}x_{n-i}% }\text{ },~n=0,1,... \] where $k$ is a positive integer and initial conditions are non zero real numbers with $\prod\limits_{i=0}^{2k}x_{n-i}\neq\mp a.$

Keywords

Difference equation Solutions Boundedness periodicity

References

  • A. Gelişken, On a system of rational difference equation, J. Computational Analysis and Applications, 23(4) (2017), 593-606.
  • D. Simsek, F. Abdullayev, On the recursive sequence x_{n+1}=((x_{n-(4k+3)})/(1+∏_{t=0}²x_{n-(k+1)t-k})), Journal of Mathematical Sciences, 6(222) (2017), 762-771.
  • D. Simsek, F. Abdullayev, On the recursive sequence x_{n+1}=((x_{n-(k+1)})/(1+x_{n}x_{n-1}...x_{n-k})), Journal of Mathematical Sciences, 234(1) (2018), 73-81.
  • E. M. Elsayed, F. Alzahrani, H. S. Alayachi, Formulas and properties of some class of nonlinear difference equation, J. Computational Analysis and Applications, 24(8) (2018),1517-1531.
  • M. B. Almatrafi, E. M. Elsayed, F. Alzahrani, Investigating some properties of a fourth order difference equation, J. Computational Analysis and Applications, 28(2) (2020), 243-253.
  • R. Abo-Zeid, Behavior of solutions of higher order difference equation, Alabama Journal of Mathematics, 42(2018), 1-10.
  • R. Karatas, Global behavior of a higher order difference equation, Computers and Mathematics with Applications, 60(2010), 830-839.
  • R. Karatas, On the solutions of the recursive sequence x_{n+1}=((αx_{n-(2k+1)})/(-a+x_{n-k}x_{n-(2k+1)})), Fasciculi Mathematici, 45(2010), 37-45.
  • S. Ergin, R. Karatas, On the solutions of the recursive sequence x_{n+1}=((αx_{n-k})/(a-∏_{i=0}^{k}x_{n-i})), Thai Journal of Mathematics, 14(2) (2016), 391-397.
  • V. L. Kocic, G. Ladas, Global Behavior of Nonlinear Difference Equations of High Order with Applications, Kluwer Academic Publishers, Dordrecht, 1993.
There are 10 citations in total.

Details

Primary Language English
Subjects Engineering
Journal Section Articles
Authors

Ramazan Karataş

Ali Gelişken

Publication Date October 15, 2021
Submission Date June 1, 2020
Acceptance Date September 20, 2021
Published in Issue Year 2021 Volume: 9 Issue: 2

Cite

APA Karataş, R., & Gelişken, A. (2021). A Solution Form of A Higher Order Difference Equation. Konuralp Journal of Mathematics, 9(2), 316-323.
AMA Karataş R, Gelişken A. A Solution Form of A Higher Order Difference Equation. Konuralp J. Math. October 2021;9(2):316-323.
Chicago Karataş, Ramazan, and Ali Gelişken. “A Solution Form of A Higher Order Difference Equation”. Konuralp Journal of Mathematics 9, no. 2 (October 2021): 316-23.
EndNote Karataş R, Gelişken A (October 1, 2021) A Solution Form of A Higher Order Difference Equation. Konuralp Journal of Mathematics 9 2 316–323.
IEEE R. Karataş and A. Gelişken, “A Solution Form of A Higher Order Difference Equation”, Konuralp J. Math., vol. 9, no. 2, pp. 316–323, 2021.
ISNAD Karataş, Ramazan - Gelişken, Ali. “A Solution Form of A Higher Order Difference Equation”. Konuralp Journal of Mathematics 9/2 (October 2021), 316-323.
JAMA Karataş R, Gelişken A. A Solution Form of A Higher Order Difference Equation. Konuralp J. Math. 2021;9:316–323.
MLA Karataş, Ramazan and Ali Gelişken. “A Solution Form of A Higher Order Difference Equation”. Konuralp Journal of Mathematics, vol. 9, no. 2, 2021, pp. 316-23.
Vancouver Karataş R, Gelişken A. A Solution Form of A Higher Order Difference Equation. Konuralp J. Math. 2021;9(2):316-23.
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