  We consider three possible approaches to formulating coordinate
transformations on position space associated with non-linear Lorentz
transformations on momentum space. The first approach uses the definition of
velocity and gives the standard Lorentz transformation. In the second method,
we translate the behavior in momentum space into position space by means of
Fourier transform. Under certain conditions, it also gives the standard Lorentz
transformation on position space. The third approach investigates the
covariance of the modified Klein-Gordon equation obtained from the dispersion
relation.
