On a Rational $(P+1)$th Order Difference Equation with Quadratic Term
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 p...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
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Emrah Evren KARA
2022-12-01
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| Series: | Universal Journal of Mathematics and Applications |
| Subjects: | |
| Online Access: | https://dergipark.org.tr/tr/download/article-file/2747138 |
| _version_ | 1797350196604043264 |
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| author | R Abo-zeıd Messaoud Berkal |
| author_facet | R Abo-zeıd Messaoud Berkal |
| author_sort | R Abo-zeıd |
| collection | DOAJ |
| description | 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. |
| first_indexed | 2024-03-08T12:42:20Z |
| format | Article |
| id | doaj.art-54bf5005a4884223a42f31fdd877d158 |
| institution | Directory Open Access Journal |
| issn | 2619-9653 |
| language | English |
| last_indexed | 2024-03-08T12:42:20Z |
| publishDate | 2022-12-01 |
| publisher | Emrah Evren KARA |
| record_format | Article |
| series | Universal Journal of Mathematics and Applications |
| spelling | doaj.art-54bf5005a4884223a42f31fdd877d1582024-01-21T09:02:37ZengEmrah Evren KARAUniversal Journal of Mathematics and Applications2619-96532022-12-015413614410.32323/ujma.11984711225On a Rational $(P+1)$th Order Difference Equation with Quadratic TermR Abo-zeıd0Messaoud Berkal1Department of Basic Science, The Higher Institute for Engineering & Technology, Al-Obour, Cairo, EgyptDepartamento de Matemática Aplicada, Universidad de Alicante, Apdo. 99, E-03080 Alicante, SpainIn 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.https://dergipark.org.tr/tr/download/article-file/2747138difference equationsgeneral solutionforbidden setinvariant setconvergence. |
| spellingShingle | R Abo-zeıd Messaoud Berkal On a Rational $(P+1)$th Order Difference Equation with Quadratic Term Universal Journal of Mathematics and Applications difference equations general solution forbidden set invariant set convergence. |
| title | On a Rational $(P+1)$th Order Difference Equation with Quadratic Term |
| title_full | On a Rational $(P+1)$th Order Difference Equation with Quadratic Term |
| title_fullStr | On a Rational $(P+1)$th Order Difference Equation with Quadratic Term |
| title_full_unstemmed | On a Rational $(P+1)$th Order Difference Equation with Quadratic Term |
| title_short | On a Rational $(P+1)$th Order Difference Equation with Quadratic Term |
| title_sort | on a rational p 1 th order difference equation with quadratic term |
| topic | difference equations general solution forbidden set invariant set convergence. |
| url | https://dergipark.org.tr/tr/download/article-file/2747138 |
| work_keys_str_mv | AT rabozeıd onarationalp1thorderdifferenceequationwithquadraticterm AT messaoudberkal onarationalp1thorderdifferenceequationwithquadraticterm |