In this paper, a new approach is proposed to investigate new type of hybrid chaos synchronization in discrete-time hyperchaotic dynamical systems. We present, based on stability theory of linear discrete-time systems and Lyapunov stability theory, a general control scheme to study the co-existence of inverse projective synchronization, inverse generalized synchronization and Q-S synchronization between arbitrary 3D hyperchaotic maps. Numerical examples and computer simulations are used to validate the theoretical results derived in this paper.