  We consider the generalized continuous-time Lyapunov equation: $$ A^*XB +
B^*XA =-Q, $$ where $Q$ is an $N\times N$ Hermitian positive definite matrix
and $A,B$ are arbitrary $N\times N$ matrices. Under some conditions, using the
coupled fixed point theorem of Bhaskar and Lakshmikantham, we establish the
existence and uniqueness of Hermitian positive definite solution for such
equation. Moreover, we provide an iteration method to find convergent sequences
which converge to the solution if one exists.
