Some Discussions on the Difference Equation xn+1=α+(xn-1m/xnk)
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...
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| Format: | Article |
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Wiley
2015-01-01
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| Series: | Journal of Function Spaces |
| Online Access: | http://dx.doi.org/10.1155/2015/737420 |
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| author | Awad A. Bakery |
| author_facet | Awad A. Bakery |
| author_sort | Awad A. Bakery |
| collection | DOAJ |
| description | 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. |
| format | Article |
| id | doaj-art-40936179244d4398a0463d0b73fe49a5 |
| institution | Kabale University |
| issn | 2314-8896 2314-8888 |
| language | English |
| publishDate | 2015-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Function Spaces |
| spelling | doaj-art-40936179244d4398a0463d0b73fe49a52025-02-03T06:11:16ZengWileyJournal of Function Spaces2314-88962314-88882015-01-01201510.1155/2015/737420737420Some Discussions on the Difference Equation xn+1=α+(xn-1m/xnk)Awad A. Bakery0Department of Mathematics, Faculty of Science and Arts, University of Jeddah (UJ), P.O. Box 355, Khulais 21921, Saudi ArabiaWe 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.http://dx.doi.org/10.1155/2015/737420 |
| spellingShingle | Awad A. Bakery Some Discussions on the Difference Equation xn+1=α+(xn-1m/xnk) Journal of Function Spaces |
| title | Some Discussions on the Difference Equation xn+1=α+(xn-1m/xnk) |
| title_full | Some Discussions on the Difference Equation xn+1=α+(xn-1m/xnk) |
| title_fullStr | Some Discussions on the Difference Equation xn+1=α+(xn-1m/xnk) |
| title_full_unstemmed | Some Discussions on the Difference Equation xn+1=α+(xn-1m/xnk) |
| title_short | Some Discussions on the Difference Equation xn+1=α+(xn-1m/xnk) |
| title_sort | some discussions on the difference equation xn 1 α xn 1m xnk |
| url | http://dx.doi.org/10.1155/2015/737420 |
| work_keys_str_mv | AT awadabakery somediscussionsonthedifferenceequationxn1axn1mxnk |