"Relativistic Inertial mass" (m' = ym) is a bogus term invented so as to make the equations look the same as the classical ones in some limited circumstances - namely, when a force is acting in the same direction as the relative velocity. If a force is acting in a different direction, to obtain a relation of the form F=mdp/dt, you need a different* so-called relativistic inertial mass.

I know of no one doing modern research in relativity using this obsolete concept.