since Velocity is equivalent to Gravity does increasing the velocity of matter increase its mass?

Question

If velocity is equivalent to gravity, does that mean particles with increasing velocity gain in actual mass associated with the curvature of space by matter?

if so, does that mass have an association with the Higgs particle?

Answer 1

Mass doesn't increase with increasing velocity. For example see If a 1kg mass was accelerated close to the speed of light would it turn into a black hole?. It is possible to write relativistic equations of motion in a form where the mass $m$ is replaced by $\gamma m$, and $\gamma m$ does increase with speed, however this approach causes as many problems as it solves and is no longer used. These days when we refer to mass we mean rest mass, and this is an invariant.

The other point we need to make is that the Higgs boson is not responsible for mass. The Higgs mechanism is resonsible for mass, and the Higgs boson that was observed at the LHC is a side effect of the Higgs mechanism. The Higgs mechanism is described using quantum field theory which is Lorentz covariant.

So there is no effect of the type you describe.