We study the dynamic phase transitions (DPT), within a mean-field approach, in the kinetic spin-1 Blume-Capel model by using the Glauber-type stochastic dynamics. The nature of the transition is characterized by investigating the behavior of the thermal variation of the dynamic order parameter and the Lyapunov exponent. The phase diagram is constructed in the temperatures (T) and single-ion anisotropy amplitude (D) plane. Our results predict first-order transitions at low temperature and large anisotropy strengths, which correspond in the phase diagram to the existence of a nonequilibrium tricritical point (TCP). We compare our results with the equilibrium phase diagram. © EDP Sciences, Società Italiana di Fisica, Springer-Verlag 2012.