  In Wang et al. (J. Optim. Theory Appl., \textbf{181}: 216--230, 2019), a
class of effective modified Newton-tpye (MN) iteration methods are proposed for
solving the generalized absolute value equations (GAVE) and it has been found
that the MN iteration method involves the classical Picard iteration method as
a special case. In the present paper, it will be claimed that a
Douglas-Rachford splitting method for AVE is also a special case of the MN
method. In addition, a class of inexact MN (IMN) iteration methods are
developed to solve GAVE. Linear convergence of the IMN method is established
and some specific sufficient conditions are presented for symmetric positive
definite coefficient matrix. Numerical results are given to demonstrate the
efficiency of the IMN iteration method.
