Tuyển tập báo cáo các nghiên cứu khoa học quốc tế ngành hóa học dành cho các bạn yêu hóa học tham khảo đề tài: Research Article Derivatives of Integrating Functions for Orthonormal Polynomials with Exponential-Type Weights | Hindawi Publishing Corporation Journal of Inequalities and Applications Volume 2009 Article ID 535849 11 pages doi 2009 535849 Research Article Advanced Discrete Halanay-Type Inequalities Stability of Difference Equations Ravi P. Agarwal 1 Young-Ho Kim 2 and S. K. Sen1 1 Department of Mathematical Sciences Florida Institute of Technology 150 West University Boulevard Melbourne FL 32901-6975 USA 2 Department of Applied Mathematics Changwon National University Changwon Kyeong-Nam 641-773 South Korea Correspondence should be addressed to Ravi P. Agarwal agarwal@ Received 7 December 2008 Accepted 21 January 2009 Recommended by Martin J. Bohner We derive new nonlinear discrete analogue of the continuous Halanay-type inequality. These inequalities can be used as basic tools in the study of the global asymptotic stability of the equilibrium of certain generalized difference equations. Copyright 2009 Ravi P. Agarwal et al. 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. 1. Introduction The investigation of stability of nonlinear difference equations with delays has attracted a lot of attention from many researchers such as Agarwal et al. 1-3 Balnov and Simeonov 4 Bay and Phat 5 Cooke and Ivanov 6 Gopalsamy 7 Liz et al. 8-10 Niamsup et al. 11 12 Mohamad and Gopalsamy 13 Pinto and Trofimchuk 14 and references sited therein. In 15 Halanay proved an asymptotic formula for the solutions of a differential inequality involving the maximum functional and applied it in the stability theory of linear systems with delay. Such an inequality was called Halanay inequality in several works. Some generalizations as well as new applications can be found for instance in Agarwal et al. 2 Gopalsamy 7 Liz et al. 8-10 Niamsup et al. 11 12 Mohamad and Gopalsamy 13 and Pinto and Trofimchuk 14 . In particular in 2 6 10 12
