On the Rational Recursive Sequence xn+1=(A+∑i=0kαixn−i)/(B+∑i=0kβixn−i)
The main objective of this paper is to study the boundedness character, the periodic character, the convergence, and the global stability of the positive solutions of the difference equation xn+1=(A+∑i=0kαixn−i)/(B+∑i=0kβixn−i), n=0,1,2,…, where A, B, αi, βi and the initial conditions x−k,...,x−1,x0...
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| Main Authors: | , |
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| Format: | Article |
| Language: | English |
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Wiley
2007-01-01
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| Series: | International Journal of Mathematics and Mathematical Sciences |
| Online Access: | http://dx.doi.org/10.1155/2007/23618 |
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| _version_ | 1832564627646447616 |
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| author | E. M. E. Zayed M. A. El-Moneam |
| author_facet | E. M. E. Zayed M. A. El-Moneam |
| author_sort | E. M. E. Zayed |
| collection | DOAJ |
| description | The main objective of this paper is to study the boundedness character, the periodic character, the convergence, and the global stability of the positive
solutions of the difference equation xn+1=(A+∑i=0kαixn−i)/(B+∑i=0kβixn−i), n=0,1,2,…, where A, B, αi, βi and the initial conditions x−k,...,x−1,x0 are arbitrary positive real numbers, while k is a positive integer number. |
| format | Article |
| id | doaj-art-b1945b5ed8ae4e109b18462615cdd6a6 |
| institution | Kabale University |
| issn | 0161-1712 1687-0425 |
| language | English |
| publishDate | 2007-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | International Journal of Mathematics and Mathematical Sciences |
| spelling | doaj-art-b1945b5ed8ae4e109b18462615cdd6a62025-02-03T01:10:36ZengWileyInternational Journal of Mathematics and Mathematical Sciences0161-17121687-04252007-01-01200710.1155/2007/2361823618On the Rational Recursive Sequence xn+1=(A+∑i=0kαixn−i)/(B+∑i=0kβixn−i)E. M. E. Zayed0M. A. El-Moneam1Mathematics Department, Faculty of Science, Zagazig University, Zagazig 44519, EgyptMathematics Department, Faculty of Science, Zagazig University, Zagazig 44519, EgyptThe main objective of this paper is to study the boundedness character, the periodic character, the convergence, and the global stability of the positive solutions of the difference equation xn+1=(A+∑i=0kαixn−i)/(B+∑i=0kβixn−i), n=0,1,2,…, where A, B, αi, βi and the initial conditions x−k,...,x−1,x0 are arbitrary positive real numbers, while k is a positive integer number.http://dx.doi.org/10.1155/2007/23618 |
| spellingShingle | E. M. E. Zayed M. A. El-Moneam On the Rational Recursive Sequence xn+1=(A+∑i=0kαixn−i)/(B+∑i=0kβixn−i) International Journal of Mathematics and Mathematical Sciences |
| title | On the Rational Recursive Sequence xn+1=(A+∑i=0kαixn−i)/(B+∑i=0kβixn−i) |
| title_full | On the Rational Recursive Sequence xn+1=(A+∑i=0kαixn−i)/(B+∑i=0kβixn−i) |
| title_fullStr | On the Rational Recursive Sequence xn+1=(A+∑i=0kαixn−i)/(B+∑i=0kβixn−i) |
| title_full_unstemmed | On the Rational Recursive Sequence xn+1=(A+∑i=0kαixn−i)/(B+∑i=0kβixn−i) |
| title_short | On the Rational Recursive Sequence xn+1=(A+∑i=0kαixn−i)/(B+∑i=0kβixn−i) |
| title_sort | on the rational recursive sequence xn 1 a ∑i 0kαixn i b ∑i 0kβixn i |
| url | http://dx.doi.org/10.1155/2007/23618 |
| work_keys_str_mv | AT emezayed ontherationalrecursivesequencexn1ai0kaixnibi0kbixni AT maelmoneam ontherationalrecursivesequencexn1ai0kaixnibi0kbixni |