Bull. Korean Math. Soc. 2013; 50(5): 1555-1565
Printed September 1, 2013
https://doi.org/10.4134/BKMS.2013.50.5.1555
Copyright © The Korean Mathematical Society.
Liguang Xu
Zhejiang University of Technology
In this paper, some new generalized discrete Halanay inequalities are established. On the basis of these new established inequalities, we obtain the attracting set and the global asymptotic stability of the nonlinear discrete systems. Our results established here extend the main results in [R. P. Agarwal, Y. H. Kim, and S. K. Sen, {\it New discrete Halanay inequalities$:$ stability of difference equations}, Commun. Appl. Anal. {\bf 12} (2008), no. 1, 83--90] and [S. Udpin and P. Niamsup, {\it New discrete type inequalities and global stability of nonlinear difference equations}, Appl. Math. Lett. {\bf 22} (2009), no. 6, 856--859].
Keywords: Halanay inequality, discrete systems, attracting set, global asymptotic stability
MSC numbers: 26D10, 26D20, 39A10, 39A70
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