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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| Main Author: | |
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| Format: | Article |
| Language: | English |
| Published: |
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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| Summary: | 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. |
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| ISSN: | 2314-8896 2314-8888 |