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}} $

Elabbasy, E. M.; El-Metwally, H.; Elsayed, E. M.

doi:10.21136/MB.2008.134057

Geodesic

Parcourir par

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}} $

Elabbasy, E. M. ; El-Metwally, H. ; Elsayed, E. M.

Mathematica Bohemica, Tome 133 (2008) no. 2, pp. 133-147.

Voir la notice de l'article provenant de la source Czech Digital Mathematics Library

Résumé

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.

MR Zbl

DOI : 10.21136/MB.2008.134057

Classification : 39A10, 39A11, 39A20, 39A22, 39A23, 39A30
Keywords: stability; periodic solution; difference equation

@article{10_21136_MB_2008_134057,
     author = {Elabbasy, E. M. and El-Metwally, H. and Elsayed, E. M.},
     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}} $},
     journal = {Mathematica Bohemica},
     pages = {133--147},
     publisher = {mathdoc},
     volume = {133},
     number = {2},
     year = {2008},
     doi = {10.21136/MB.2008.134057},
     mrnumber = {2428309},
     zbl = {1199.39028},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.21136/MB.2008.134057/}
}

TY  - JOUR
AU  - Elabbasy, E. M.
AU  - El-Metwally, H.
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
SP  - 133
EP  - 147
VL  - 133
IS  - 2
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/articles/10.21136/MB.2008.134057/
DO  - 10.21136/MB.2008.134057
LA  - en
ID  - 10_21136_MB_2008_134057
ER  -

%0 Journal Article
%A Elabbasy, E. M.
%A El-Metwally, H.
%A Elsayed, E. M.
%T 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}} $
%J Mathematica Bohemica
%D 2008
%P 133-147
%V 133
%N 2
%I mathdoc
%U http://geodesic.mathdoc.fr/articles/10.21136/MB.2008.134057/
%R 10.21136/MB.2008.134057
%G en
%F 10_21136_MB_2008_134057

Elabbasy, E. M.; El-Metwally, H.; 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, Tome 133 (2008) no. 2, pp. 133-147. doi : 10.21136/MB.2008.134057. http://geodesic.mathdoc.fr/articles/10.21136/MB.2008.134057/

Cité par Sources :