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Recently, there has been a number of extensive works on mixed spin Ising systems both theoretically and experimentally,since such systems are important magnetic materials for technology of thermo-magnetic recording. Ferrimagnets have several sublattices with a finite resultant moment. However, they normally take complicated magnetic structures. Because of the complexity of the structures, the author applied the standard mean-field theory for mixed spin Ising ferrimagnets.The mean-field approximation is an adequate starting point as it describes cooperative phenomena in which the effect of the ordering interaction is represented by that of a mean field proportional to the average net magnetic moment of a magnetic system.In this work, we have examined the effect of a single-ion anisotropy as well as an applied magnetic field on the existence and location of a compensation temperature to clarify the characteristic features in a series of molecular-based magnets. So, our investigations predict the possibility of many compensation points at low temperatures depending mainly on the negative and positive values of both anisotropies, and some characteristic values of the external fields.