A Part-Metric-Related Inequality Chain and Application to the Stability Analysis of Difference Equation

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...

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Main Authors: Maobin Yang, Huaiyi Liu, Xiaofan Yang
Format: Article
Language:English
Published: SpringerOpen 2007-03-01
Series:Journal of Inequalities and Applications
Online Access:http://dx.doi.org/10.1155/2007/19618
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spelling doaj-9e0d03fba2dc4ac2bd245defd8941baf2020-11-24T21:40:16ZengSpringerOpenJournal of Inequalities and Applications1025-58341029-242X2007-03-01200710.1155/2007/19618A Part-Metric-Related Inequality Chain and Application to the Stability Analysis of Difference EquationMaobin YangHuaiyi LiuXiaofan YangWe 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.http://dx.doi.org/10.1155/2007/19618
collection DOAJ
language English
format Article
sources DOAJ
author Maobin Yang
Huaiyi Liu
Xiaofan Yang
spellingShingle Maobin Yang
Huaiyi Liu
Xiaofan Yang
A Part-Metric-Related Inequality Chain and Application to the Stability Analysis of Difference Equation
Journal of Inequalities and Applications
author_facet Maobin Yang
Huaiyi Liu
Xiaofan Yang
author_sort Maobin Yang
title A Part-Metric-Related Inequality Chain and Application to the Stability Analysis of Difference Equation
title_short A Part-Metric-Related Inequality Chain and Application to the Stability Analysis of Difference Equation
title_full A Part-Metric-Related Inequality Chain and Application to the Stability Analysis of Difference Equation
title_fullStr A Part-Metric-Related Inequality Chain and Application to the Stability Analysis of Difference Equation
title_full_unstemmed A Part-Metric-Related Inequality Chain and Application to the Stability Analysis of Difference Equation
title_sort part-metric-related inequality chain and application to the stability analysis of difference equation
publisher SpringerOpen
series Journal of Inequalities and Applications
issn 1025-5834
1029-242X
publishDate 2007-03-01
description 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.
url http://dx.doi.org/10.1155/2007/19618
work_keys_str_mv AT maobinyang apartmetricrelatedinequalitychainandapplicationtothestabilityanalysisofdifferenceequation
AT huaiyiliu apartmetricrelatedinequalitychainandapplicationtothestabilityanalysisofdifferenceequation
AT xiaofanyang apartmetricrelatedinequalitychainandapplicationtothestabilityanalysisofdifferenceequation
AT maobinyang partmetricrelatedinequalitychainandapplicationtothestabilityanalysisofdifferenceequation
AT huaiyiliu partmetricrelatedinequalitychainandapplicationtothestabilityanalysisofdifferenceequation
AT xiaofanyang partmetricrelatedinequalitychainandapplicationtothestabilityanalysisofdifferenceequation
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