Open Access

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

Journal of Inequalities and Applications20072007:019618

DOI: 10.1155/2007/19618

Received: 8 October 2006

Accepted: 14 December 2006

Published: 20 March 2007

Abstract

We find a new part-metric-related inequality of the form https://static-content.springer.com/image/art%3A10.1155%2F2007%2F19618/MediaObjects/13660_2006_Article_1679_IEq1_HTML.gif https://static-content.springer.com/image/art%3A10.1155%2F2007%2F19618/MediaObjects/13660_2006_Article_1679_IEq2_HTML.gif https://static-content.springer.com/image/art%3A10.1155%2F2007%2F19618/MediaObjects/13660_2006_Article_1679_IEq3_HTML.gif , where https://static-content.springer.com/image/art%3A10.1155%2F2007%2F19618/MediaObjects/13660_2006_Article_1679_IEq4_HTML.gif . We then apply this result to show that https://static-content.springer.com/image/art%3A10.1155%2F2007%2F19618/MediaObjects/13660_2006_Article_1679_IEq5_HTML.gif is a globally asymptotically stable equilibrium of the rational difference equation https://static-content.springer.com/image/art%3A10.1155%2F2007%2F19618/MediaObjects/13660_2006_Article_1679_IEq6_HTML.gif https://static-content.springer.com/image/art%3A10.1155%2F2007%2F19618/MediaObjects/13660_2006_Article_1679_IEq7_HTML.gif , https://static-content.springer.com/image/art%3A10.1155%2F2007%2F19618/MediaObjects/13660_2006_Article_1679_IEq8_HTML.gif https://static-content.springer.com/image/art%3A10.1155%2F2007%2F19618/MediaObjects/13660_2006_Article_1679_IEq9_HTML.gif .

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Authors’ Affiliations

(1)
College of Computer Science, Chongqing University

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Copyright

© Xiaofan Yang et al. 2007

This article is published under license to BioMed Central Ltd. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.