Comparison theorems for anticipated BSDEs with non-Lipschitz coefficients

We study comparison theorems for one dimensional anticipated backward stochastic differential equations under one kind of non-Lipschitz assumption. In the results, the generator functions are allowed to contain the anticipated term of z, neither generator function needs to be necessarily monotone in the anticipated term of y, and the anticipated times of the anticipated terms of (y,z) in one generator function can differ from those in the other.