  We introduce the concept of k-strictly convexity to describe the accurate
convexity of convex domains some directions of which boundary may be flat.
Basing this accurate convexity, we construct sub-solutions the Dirichlet
problem for some degenerate-singular Monge-Amp\`ere type equations and prove
the sharp boundary estimates for convex viscosity solutions of the problem. As
a result, we obtain the optimal global H\"older regularity of the convex
viscosity solutions.
