The special relativity with wave equation

Question

With the formation of Einstein special relativity, $E^2 = p^2c^2 + m^2c^4$, could the term of mass be replaced with the De Broglie equation of material waves while $p$, momentum, be replaced with the momentum of the wave as $hk$ where $k$ is the wavenumbers?

Answer 1

You can't do that because it's the wrong "mass". The $m$ in the formula for $E^2$ is rest mass, not relativistic mass.