Bulletin of the
Korean Mathematical Society
BKMS

ISSN(Print) 1015-8634 ISSN(Online) 2234-3016

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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.

Generalized discrete Halanay inequalities and the asymptotic behavior of nonlinear discrete systems

Liguang Xu

Zhejiang University of Technology

Abstract

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