[jeffreyH (OP)]

There is a definition of inertial mass in Special Relativity by N.M.J. Woodhouse on page 128.

"Suppose that a particle of rest mass m has velocity v relative to some inertial coordinate system. The quantities m_I = mγ(v) and p = m_Iv are the inertial mass and the three-momentum of the particle relative to the inertial coordinate system.

Four-momentum conservation is equivalent to conservation of inertial mass and of three-momentum (in every inertial coordinate system). The new feature of the relativistic theory is that the inertial mass of a particle increases with its velocity, albeit only very slightly for velocities much less than that of light.

Rest mass is a scalar--by its operational definition, it is an intrinsic quantity--but inertial mass is different in different inertial coordinate systems. Rest mass and inertial mass are equal for a particle at rest."

As @Janus has mentioned is this not energy that increases instead of mass?

[jeffreyH (OP)]

Here is something related on transformation of forces.
http://www.sciencebits.com/Transformation-Forces-Relativity
Also
http://bado-shanai.net/Map%20of%20Physics/mopRelativityofForce.htm