On the difference equation

Elmetwally M. Elabbasy; Hamdy El-Metwally; E. M. Elsayed

Mathematica Bohemica (2008)

  • Volume: 133, Issue: 2, page 133-147
  • ISSN: 0862-7959

Abstract

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In this paper we investigate the global convergence result, boundedness and periodicity of solutions of the recursive sequence where the parameters and for are positive real numbers and the initial conditions are arbitrary positive numbers.

How to cite

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Elabbasy, Elmetwally M., El-Metwally, Hamdy, and Elsayed, E. M.. "On the difference equation $x_{n+1}=\dfrac{a_{0}x_{n}+a_{1}x_{n-1}+\dots +a_{k}x_{n-k}}{b_{0}x_{n}+b_{1}x_{n-1}+\dots +b_{k}x_{n-k}} $." Mathematica Bohemica 133.2 (2008): 133-147. <http://eudml.org/doc/250521>.

@article{Elabbasy2008,
abstract = {In this paper we investigate the global convergence result, boundedness and periodicity of solutions of the recursive sequence \[ x\_\{n+1\}=\frac\{a\_\{0\}x\_\{n\}+a\_\{1\}x\_\{n-1\}+\dots +a\_\{k\}x\_\{n-k\}\}\{b\_\{0\}x\_\{n\}+b\_\{1\}x\_\{n-1\}+\dots +b\_\{k\}x\_\{n-k\}\},\,\,\,n=0,1,\dots \,\ \] where the parameters $ a_\{i\}$ and $b_\{i\}$ for $i=0,1,\dots ,k$ are positive real numbers and the initial conditions $x_\{-k\},x_\{-k+1\},\dots ,x_\{0\}$ are arbitrary positive numbers.},
author = {Elabbasy, Elmetwally M., El-Metwally, Hamdy, Elsayed, E. M.},
journal = {Mathematica Bohemica},
keywords = {stability; periodic solution; difference equation; stability; periodic solution; rational difference equation; global convergence; boundedness; recursive sequence},
language = {eng},
number = {2},
pages = {133-147},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {On the difference equation $x_\{n+1\}=\dfrac\{a_\{0\}x_\{n\}+a_\{1\}x_\{n-1\}+\dots +a_\{k\}x_\{n-k\}\}\{b_\{0\}x_\{n\}+b_\{1\}x_\{n-1\}+\dots +b_\{k\}x_\{n-k\}\} $},
url = {http://eudml.org/doc/250521},
volume = {133},
year = {2008},
}

TY - JOUR
AU - Elabbasy, Elmetwally M.
AU - El-Metwally, Hamdy
AU - Elsayed, E. M.
TI - On the difference equation $x_{n+1}=\dfrac{a_{0}x_{n}+a_{1}x_{n-1}+\dots +a_{k}x_{n-k}}{b_{0}x_{n}+b_{1}x_{n-1}+\dots +b_{k}x_{n-k}} $
JO - Mathematica Bohemica
PY - 2008
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 133
IS - 2
SP - 133
EP - 147
AB - In this paper we investigate the global convergence result, boundedness and periodicity of solutions of the recursive sequence \[ x_{n+1}=\frac{a_{0}x_{n}+a_{1}x_{n-1}+\dots +a_{k}x_{n-k}}{b_{0}x_{n}+b_{1}x_{n-1}+\dots +b_{k}x_{n-k}},\,\,\,n=0,1,\dots \,\ \] where the parameters $ a_{i}$ and $b_{i}$ for $i=0,1,\dots ,k$ are positive real numbers and the initial conditions $x_{-k},x_{-k+1},\dots ,x_{0}$ are arbitrary positive numbers.
LA - eng
KW - stability; periodic solution; difference equation; stability; periodic solution; rational difference equation; global convergence; boundedness; recursive sequence
UR - http://eudml.org/doc/250521
ER -

References

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Citations in EuDML Documents

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  1. E. M. E. Zayed, M. A. El-Moneam, On the rational recursive sequence

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