  We quantitatively analyze the meson mass inequality relations of two
dimensional gauged four fermi models in the large N limit. The class of models
we study includes the 't Hooft model, the chiral and non-chiral Gross-Neveu
models as special points in the space of field theories. Cases where the chiral
symmetry is spontaneously or explicitly broken are both studied. We study the
meson mass inequality quantitatively and define a susceptibility which allows
us to systematically analyze the inequality. In the generalized Gross-Neveu
model limit, we derive an analytic expression for this susceptibility. Even
though no analytic proof of the validity of the classic mass inequality exists
for the generic case, the mass inequality is found to be positive throughout
most of the parameter space. We point out that the inequality might be negative
in certain cases.
