  Beyond-constant-mass approximation solutions for magnetically catalyzed
fermion and scalar masses are found in a gauge Higgs-Yukawa theory in the
presence of a constant magnetic field. The obtained fermion masses are several
orders of magnitude larger than those found in the absence of Yukawa
interactions. The masses obtained within the beyond-constant-mass approximation
exactly reduce to the results within the constant-mass approach when the
condition $\nu \ln (\frac{1}{\hat{m}^{2}})\ll 1$ is satisfied. Possible
applications to early universe physics and condensed matter are discussed.
