  In this paper we shall prove the existence, uniqueness and global
H$\ddot{o}$lder continuity for the Dirichlet problem of a class of
Monge-Amp\`ere type equations which may be degenerate and singular on the
boundary of convex domains.
  We will establish a relation of the H$\ddot{o}$lder exponent for the
solutions with the convexity for the domains.
