On the rational recursive sequence x n + 1 = A + ∑ i = 0 k α i x n - i / ∑ i = 0 k β i x n - i

E. M. E. Zayed; M. A. El-Moneam

Mathematica Bohemica (2008)

  • Volume: 133, Issue: 3, page 225-239
  • ISSN: 0862-7959

Abstract

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The main objective of this paper is to study the boundedness character, the periodic character, the convergence and the global stability of positive solutions of the difference equation x n + 1 = A + ∑ i = 0 k α i x n - i / ∑ i = 0 k β i x n - i , n = 0 , 1 , 2 , ⋯ where the coefficients A , α i , β i and the initial conditions x - k , x - k + 1 , ⋯ , x - 1 , x 0 are positive real numbers, while k is a positive integer number.

How to cite

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Zayed, E. M. E., and El-Moneam, M. A.. "On the rational recursive sequence $ \ x_{n+1}=\Big ( A+\sum _{i=0}^k\alpha _ix_{n-i}\Big ) \Big / \sum _{i=0}^k\beta _ix_{n-i} $." Mathematica Bohemica 133.3 (2008): 225-239. <http://eudml.org/doc/250538>.

@article{Zayed2008,
abstract = {The main objective of this paper is to study the boundedness character, the periodic character, the convergence and the global stability of positive solutions of the difference equation \[ x\_\{n+1\}=\bigg ( A+\sum \_\{i=0\}^k\alpha \_ix\_\{n-i\}\bigg ) \Big / \sum \_\{i=0\}^k\beta \_ix\_\{n-i\},\ \ n=0,1,2,\dots \] where the coefficients $A$, $\alpha _i$, $\beta _i$ and the initial conditions $x_\{-k\},x_\{-k+1\},\dots ,x_\{-1\},x_0$ are positive real numbers, while $k$ is a positive integer number.},
author = {Zayed, E. M. E., El-Moneam, M. A.},
journal = {Mathematica Bohemica},
keywords = {difference equations; boundedness character; period two solution; convergence; global stability; boundedness character; period two solution; convergence; global stability; rational difference equation; positive solutions},
language = {eng},
number = {3},
pages = {225-239},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {On the rational recursive sequence $ \ x_\{n+1\}=\Big ( A+\sum _\{i=0\}^k\alpha _ix_\{n-i\}\Big ) \Big / \sum _\{i=0\}^k\beta _ix_\{n-i\} $},
url = {http://eudml.org/doc/250538},
volume = {133},
year = {2008},
}

TY - JOUR
AU - Zayed, E. M. E.
AU - El-Moneam, M. A.
TI - On the rational recursive sequence $ \ x_{n+1}=\Big ( A+\sum _{i=0}^k\alpha _ix_{n-i}\Big ) \Big / \sum _{i=0}^k\beta _ix_{n-i} $
JO - Mathematica Bohemica
PY - 2008
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 133
IS - 3
SP - 225
EP - 239
AB - The main objective of this paper is to study the boundedness character, the periodic character, the convergence and the global stability of positive solutions of the difference equation \[ x_{n+1}=\bigg ( A+\sum _{i=0}^k\alpha _ix_{n-i}\bigg ) \Big / \sum _{i=0}^k\beta _ix_{n-i},\ \ n=0,1,2,\dots \] where the coefficients $A$, $\alpha _i$, $\beta _i$ and the initial conditions $x_{-k},x_{-k+1},\dots ,x_{-1},x_0$ are positive real numbers, while $k$ is a positive integer number.
LA - eng
KW - difference equations; boundedness character; period two solution; convergence; global stability; boundedness character; period two solution; convergence; global stability; rational difference equation; positive solutions
UR - http://eudml.org/doc/250538
ER -

References

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