Abstract: On the basis of constructing the functions of class S_α it is proved that the viscosity solutions of parabolic equations belong to the functions of class S_α under certain conditions. Thus the discu ssion of studying viscosity solutions is converted to that of studying the functions of class S_α. The Aleksandrov-Bakel'man-Pucci-Krylov-Tso maximum principle is generalized to a more general one and it is proved that the functions of class S_α obey the generalized Aleksandrov-Bakel'man-Pucci-Krylov-T so maximum principle, by means of which some regularity results to the viscosity solutions of fully nonlinear parabolic equations are obtained.

Key words: maximum principle, viscosity solutions, regularity