  By using the Picard iteration scheme, this article establishes the existence
and uniqueness theory for solutions to stochastic functional differential
equations driven by G-Browniain motion. Assuming the monotonicity conditions,
the boundedness and existence-uniqueness results of solutions have been
derived. The error estimation between Picard approximate solution $y^k(t)$ and
exact solution $y(t)$ has been determined. The $L^2_G$ and exponential
estimates have been obtained. The theory has been further generalized to weak
monotonicity conditions. The existence, uniqueness and exponential estimate
under the weak monotonicity conditions have been inaugurated.
