In this paper,by using the inequality of Liu,the almost T-stability of the Halpern iterative algorithm due to Xu for nonexpansive mappings is investigated in Banach spaces.

Under suitable conditions,the existence and uniqueness of solutions of the that inclusion and the convergence and almost stability of the sequence generated by the iterative al.

The sufficient condition for almost sure stability of Markov jump linear systems with disturbance;

The almost surely exponential stability of a Hopfield type stochastic neural network was studied by using the Lyapunov function and It formula,and a theorem and two corollaries were proved.

The almost surely exponential stability of stochastic recurrent neural networks with time-varying delays is investigated.

The problems of p-Moment exponential stability and almost sure exponential stability of nonlinear stochastic impulsive systems with Markovian switching are studied.

In view of the character of saturation of output functions of the cellular neural networks, the method decomposing the state to sub-regions is adopted to study almost sure exponential stability on a class delayed cellular neural networks which are in the noised environment.

Some algebraic criterion of almost sure exponential stability are obtained when the disturbance term of the network satisfies the Lipschitz condition.