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Some Discussions on the Difference Equation xn+1=α+(xn-1mxnk)
Author
Source
Issue
Vol. 2015, Issue 2015 (31 Dec. 2015), pp.1-9, 9 p.
Publisher
Hindawi Publishing Corporation
Publication Date
2015-05-10
Country of Publication
Egypt
No. of Pages
9
Main Subjects
Abstract EN
We give in this work the sufficient conditions on the positive solutions of the difference equation xn+1=α+(xn-1m/xnk), n=0,1,…, where α, k, and m∈(0,∞) under positive initial conditions x-1, x0 to be bounded, α-convergent, the equilibrium point to be globally asymptotically stable and that every positive solution converges to a prime two-periodic solution.
Our results coincide with that known for the cases m=k=1 of Amleh et al.
(1999) and m=1 of Hamza and Morsy (2009).
We offer improving conditions in the case of m=1 of Gümüs and Öcalan (2012) and explain our results by some numerical examples with figures.
American Psychological Association (APA)
Bakery, Awad A.. 2015. Some Discussions on the Difference Equation xn+1=α+(xn-1mxnk). Journal of Function Spaces،Vol. 2015, no. 2015, pp.1-9.
https://search.emarefa.net/detail/BIM-1068314
Modern Language Association (MLA)
Bakery, Awad A.. Some Discussions on the Difference Equation xn+1=α+(xn-1mxnk). Journal of Function Spaces No. 2015 (2015), pp.1-9.
https://search.emarefa.net/detail/BIM-1068314
American Medical Association (AMA)
Bakery, Awad A.. Some Discussions on the Difference Equation xn+1=α+(xn-1mxnk). Journal of Function Spaces. 2015. Vol. 2015, no. 2015, pp.1-9.
https://search.emarefa.net/detail/BIM-1068314
Data Type
Journal Articles
Language
English
Notes
Includes bibliographical references
Record ID
BIM-1068314