On a Rational $(P+1)$th Order Difference Equation with Quadratic Term

Messaoud Berkal; R Abo-zeıd

doi:10.32323/ujma.1198471

EN

On a Rational $(P+1)$th Order Difference Equation with Quadratic Term

Abstract

In this paper, we derive the forbidden set and determine the solutions of the difference equation that contains a quadratic term \begin{equation*} x_{n+1}=\frac{x_{n}x_{n-p}}{ax_{n-(p-1)}+bx_{n-p}},\quad n\in\mathbb{N}_0, \end{equation*} where the parameters $a$ and $b$ are real numbers, $p$ is a positive integer and the initial conditions $x_{-p}$, $x_{-p+1}$, $\cdots$, $x_{-1}$, $x_{0}$ are real numbers.

Keywords

Difference equations, General solution, Forbidden set, Invariant set, convergence.

References

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Details

Primary Language

English

Subjects

Mathematical Sciences

Journal Section

Research Article

Authors

Messaoud Berkal ^*
Algeria

R Abo-zeıd
Egypt

Publication Date

December 29, 2022

Submission Date

November 2, 2022

Acceptance Date

December 7, 2022

Published in Issue

Year 2022 Volume: 5 Number: 4

DOI

https://doi.org/10.32323/ujma.1198471

IZ

https://izlik.org/JA73XY55DF

APA

Berkal, M., & Abo-zeıd, R. (2022). On a Rational $(P+1)$th Order Difference Equation with Quadratic Term. Universal Journal of Mathematics and Applications, 5(4), 136-144. https://doi.org/10.32323/ujma.1198471

AMA

1.Berkal M, Abo-zeıd R. On a Rational $(P+1)$th Order Difference Equation with Quadratic Term. Univ. J. Math. Appl. 2022;5(4):136-144. doi:10.32323/ujma.1198471

Chicago

Berkal, Messaoud, and R Abo-zeıd. 2022. “On a Rational $(P+1)$th Order Difference Equation With Quadratic Term”. Universal Journal of Mathematics and Applications 5 (4): 136-44. https://doi.org/10.32323/ujma.1198471.

EndNote

Berkal M, Abo-zeıd R (December 1, 2022) On a Rational $(P+1)$th Order Difference Equation with Quadratic Term. Universal Journal of Mathematics and Applications 5 4 136–144.

IEEE

[1]M. Berkal and R. Abo-zeıd, “On a Rational $(P+1)$th Order Difference Equation with Quadratic Term”, Univ. J. Math. Appl., vol. 5, no. 4, pp. 136–144, Dec. 2022, doi: 10.32323/ujma.1198471.

ISNAD

Berkal, Messaoud - Abo-zeıd, R. “On a Rational $(P+1)$th Order Difference Equation With Quadratic Term”. Universal Journal of Mathematics and Applications 5/4 (December 1, 2022): 136-144. https://doi.org/10.32323/ujma.1198471.

JAMA

1.Berkal M, Abo-zeıd R. On a Rational $(P+1)$th Order Difference Equation with Quadratic Term. Univ. J. Math. Appl. 2022;5:136–144.

MLA

Berkal, Messaoud, and R Abo-zeıd. “On a Rational $(P+1)$th Order Difference Equation With Quadratic Term”. Universal Journal of Mathematics and Applications, vol. 5, no. 4, Dec. 2022, pp. 136-44, doi:10.32323/ujma.1198471.

Vancouver

1.Messaoud Berkal, R Abo-zeıd. On a Rational $(P+1)$th Order Difference Equation with Quadratic Term. Univ. J. Math. Appl. 2022 Dec. 1;5(4):136-44. doi:10.32323/ujma.1198471