{"references": ["A. Halanay, Differential Equations: Stability, Oscillations, Time Lags,\nAcademic Press, New York, NY, USA, 1966.", "R. Agarwal, Y. Kim, and S. Sen, Advanced Discrete Halanay-Type\nInequalities: Stability of Difference Equations, Volume 2009, Article ID\n535849, 11 pages doi:10.1155/2009/535849.", "J. L, On Some New Impulsive Integral Inequalities, Journal of Inequalities\nand Applications Volume 2008, Article ID 312395, 8 pages\ndoi:10.1155/2008/312395.", "D. Xu, Z. Yang, Impulsive delay diffrential inequality and stability of\nneural networks, Journal of Mathematical Analysis and Applications, 305\n(2005) 107-120.", "Z. Ma, X. Wang, A new singular impulsive delay dierential inequality\nand its application, Journal of Inequalities and Applications, Accepted\nArticle.", "W. Cheung, D. Zhao, Gronwall-Bellman-Type Integral Inequalities and\napplications to BVPs, Journal of Inequalities and Applications, Accepted\nArticle.", "Y. Yang, J. Cao, Solving Quadratic Programming Problems by Delayed\nProjection Neural Network, IEEE Transactions on neural metworks. 17\n(2006) 1630-1634.", "X. Hu, Applications of the general projection neural network in solving\nextended linear-quadratic programming problems with linear constraints,\nNeurocomputing (2008), doi:10.1016/j.neucom.2008.02.016", "Y. Yang, J. Cao, A feedback neural network for solving convex ..., Appl.\nMath. Comput. (2008), doi:10.1016/j.amc.2007.12.029\n[10] Li P et al., Delay-dependent robust BIBO stabilization ..., Chaos,\nSolitons and Fractals (2007), doi:10.1016/j.chaos.2007.08.059\n[11] O. Lipovan, A Retarded Gronwall-Like Inequality and Its Applications,\nJournal of Mathematical Analysis and Applications 252 (2000) 389-401\n.\n[12] R. Agarwal, S. Deng and W. Zhang, Generalization of a retarded\nGronwall-like inequality and its applications, Applied Mathematics and\nComputation 165 (2005) 599-612.\n[13] A. Gallo, A. Piccirillo, About new analogies of GronwallCBellmanCBihari\ntype inequalities for discontinuous functions and estimated solutions\nfor impulsive differential systems, Nonlinear Analysis 67 (2007) 1550-\n1559.\n[14] W. Wang, A generalized retarded Gronwall-like inequality in two variables\nand applications to BVP, Applied Mathematics and Computation\n191 (2007) 144-154.\n[15] W. Zhang, S. Deng, Projected GronwallCBellmans inequality for integral\nfunctions, Mathematical and Computer Modelling. 34 (2001) 393-\n402.\n[16] X. Mao, Stochastic Differential Equations and Applications, Horwood\nPublication, Chichester, 1997.\n[17] Yonghui Sun,Jinde Cao, pth moment exponential stability of stochastic\nrecurrent neural networks with time-varying delays, Nonlinear Analysis:\nRealWorld Applications, 8 (2007) 1171-1185.\n[18] Y. Xia, Z. Huang, M. Han, Exponential p-stability of delayed Cohen-\nGrossberg-type BAM neural networks with impulses, Chaos, Solitons and\nFractals, 38 (2008) 806-818.\n[19] L. Sheng, H. Yang, Exponential synchronization of a class of neural\nnetworks with mixed time-varying delays and impulsive effects, Neurocomputing,\n71 (2008) 3666-3674.\n[20] H. Kopka and P. W. Daly, A Guide to LATEX, 3rd ed. Harlow, England:\nAddison-Wesley, 1999."]}

In this paper, some new nonlinear generalized Gronwall-Bellman-Type integral inequalities with mixed time delays are established. These inequalities can be used as handy tools to research stability problems of delayed differential and integral dynamic systems. As applications, based on these new established inequalities, some p-stable results of a integro-differential equation are also given. Two numerical examples are presented to illustrate the validity of the main results.