A matrix $P{in}mathbb{R}^{n{ imes}n}$ is called a generalized reflection if $P^T=P$ and $P^2=I$. An $n{ imes}n$ matrix A is said to be a reflexive (anti-reflexive) with respect to P if A = PAP (A = -PAP). In the present paper, two iterative methods are derived for solving the generalized Sylvester matrix equation ${sum}_{i=1}^{p}A_iXB_i+{sum}_{j=1}^{q}C_jYD_j=E$, (including the Sylvester and Lyapunov matrix equations as special cases) over reflexive and anti-reflexive matrices respectively. It is proven that the iterative methods, respectively, consistently converge to the reflexive and anti-reflexive solutions of the matrix equation for any initial reflexive and anti-reflexive matrices. Finally, a numerical example is given to demonstrate the effectiveness of the derived methods.