Mean square asymptotic stability of stochastic delayed systems by fixed point theory

In this paper, we consider a nonlinear neutral stochastic system with variable delays and give conditions to ensure that the zero solution is asymptotically mean square stable by m eans of fixed point theory. These conditions do not require the roundedness of delays, nor do they ask for a fixed sign on the coefficient functions. An asymptotically mean square stable theorem with necessary and sufficient condition is proved. Some results are improved and generalized