A Part-Metric-Related Inequality Chain and Application to the Stability Analysis of Difference Equation
We find a new part-metric-related inequality of the form min{ai,1/ai:1≤i≤5}≤((1+w)a1a2a3+a4+a5)/(a1a2+a1a3+a2a3+wa4a5)≤max{ai,1/ai:1≤i≤5}, where 1≤w≤2. We then apply this result to show that c^=1 is a globally asymptotically stable equilibrium of the rationa...
| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
| Published: |
SpringerOpen
2007-03-01
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| Series: | Journal of Inequalities and Applications |
| Online Access: | http://dx.doi.org/10.1155/2007/19618 |
| Summary: | We find a new part-metric-related inequality of the form min{ai,1/ai:1≤i≤5}≤((1+w)a1a2a3+a4+a5)/(a1a2+a1a3+a2a3+wa4a5)≤max{ai,1/ai:1≤i≤5}, where 1≤w≤2. We then apply this result to show that c^=1 is a globally asymptotically stable equilibrium of the rational difference equation xn=(xn−1+xn−2+(1+w)xn−3xn−4xn−5)/(wxn−1xn−2+xn−3xn−4+xn−3xn−5+xn−4xn−5), n=1,2,…,a0,a−1,a−2,a−3,a−4>0. |
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| ISSN: | 1025-5834 1029-242X |