Representation of Solutions to a Two-Dimensional System of Difference Equations

Mehmet Gümüş; Raafat Abo-zeid; Ana Catarina Carapito

Representation of Solutions to a Two-Dimensional System of Difference Equations

Abstract

In this paper, we conduct a comprehensive investigation to introduce a representation to the well-defined solutions of the following system of higher-order difference equations $$ x_{n+1}=\frac{y_{n-1}(a_1y_{n-1}+b_1x_{n-3})}{c_1x_{n-3}+d_1y_{n-1}},\quad y_{n+1}=\frac{x_{n-1}(a_2x_{n-1}+b_2y_{n-3})}{c_2y_{n-3}+d_2x_{n-1}},\quad n=0,1,\ldots, $$ where $a_i,b_i,c_i,d_i$, $i=1,2$, and the initial values $x_{-3},...,x_{0},y_{-3},...,y_{0}$ are real numbers such that $|b_1|+|b_2|+|c_1|+|c_2|\neq0$. Finally, the theoretical findings of the study are supported by some numerical examples.

Keywords

Supporting Institution

This work was partially supported by the Portuguese Foundation for Science and Technology (FCT- Fundação para a Ciência e a Tecnologia), through the Center of Mathematics and Applications of University of Beira Interior (CMA-UBI), within Project UIDB/00212/2020.

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Details

Primary Language

English

Subjects

Applied Mathematics (Other)

Journal Section

Research Article

Authors

Mehmet Gümüş
0000-0002-7447-479X
Türkiye

Raafat Abo-zeid
Egypt

Ana Catarina Carapito ^*
Portugal

Early Pub Date

April 29, 2025

Publication Date

April 30, 2025

Submission Date

February 25, 2025

Acceptance Date

March 17, 2025

Published in Issue

Year 2025 Volume: 13 Number: 1

IZ

https://izlik.org/JA68GK96TK

Cite

RIS / Bibtex

APA

Gümüş, M., Abo-zeid, R., & Carapito, A. C. (2025). Representation of Solutions to a Two-Dimensional System of Difference Equations. Konuralp Journal of Mathematics, 13(1), 108-116. https://izlik.org/JA68GK96TK

AMA

1.Gümüş M, Abo-zeid R, Carapito AC. Representation of Solutions to a Two-Dimensional System of Difference Equations. Konuralp J. Math. 2025;13(1):108-116. https://izlik.org/JA68GK96TK

Chicago

Gümüş, Mehmet, Raafat Abo-zeid, and Ana Catarina Carapito. 2025. “Representation of Solutions to a Two-Dimensional System of Difference Equations”. Konuralp Journal of Mathematics 13 (1): 108-16. https://izlik.org/JA68GK96TK.

EndNote

Gümüş M, Abo-zeid R, Carapito AC (April 1, 2025) Representation of Solutions to a Two-Dimensional System of Difference Equations. Konuralp Journal of Mathematics 13 1 108–116.

IEEE

[1]M. Gümüş, R. Abo-zeid, and A. C. Carapito, “Representation of Solutions to a Two-Dimensional System of Difference Equations”, Konuralp J. Math., vol. 13, no. 1, pp. 108–116, Apr. 2025, [Online]. Available: https://izlik.org/JA68GK96TK

ISNAD

Gümüş, Mehmet - Abo-zeid, Raafat - Carapito, Ana Catarina. “Representation of Solutions to a Two-Dimensional System of Difference Equations”. Konuralp Journal of Mathematics 13/1 (April 1, 2025): 108-116. https://izlik.org/JA68GK96TK.

JAMA

1.Gümüş M, Abo-zeid R, Carapito AC. Representation of Solutions to a Two-Dimensional System of Difference Equations. Konuralp J. Math. 2025;13:108–116.

MLA

Gümüş, Mehmet, et al. “Representation of Solutions to a Two-Dimensional System of Difference Equations”. Konuralp Journal of Mathematics, vol. 13, no. 1, Apr. 2025, pp. 108-16, https://izlik.org/JA68GK96TK.

Vancouver

1.Mehmet Gümüş, Raafat Abo-zeid, Ana Catarina Carapito. Representation of Solutions to a Two-Dimensional System of Difference Equations. Konuralp J. Math. [Internet]. 2025 Apr. 1;13(1):108-16. Available from: https://izlik.org/JA68GK96TK