The magnetic properties of a three-sublattice mixed-spin Heisenberg ferromagnetic and ferrimagnetic system are investigated with the help of the Green's function technique in order to clarify some characteristic magnetic behaviors of Prussian-blue compounds. Various types of magnetization curves are obtained, which exhibits one- and two-compensation temperatures. The first-order phase transitions from ferrimagnetic to ferromagnetic state have been observed. There are zero-temperature quantum fluctuations for the ferrimagnet at the absolute state while not for ferromagnet. Moreover, in the case of ferrimagnet, inverted magnetic hysteresis loop with negative coercivity is observed at a certain temperature range and the coercivity takes the value zero at the compensation point. © 2014 Elsevier B.V.