  In this paper, firstly, by solving the Riemann problem of the zero-pressure
flow in gas dynamics with a flux approximation, we construct parameterized
delta-shock and constant density solutions, then we show that, as the flux
perturbation vanishes, they converge to the delta-shock and vacuum state
solutions of the zero-pressure flow, respectively. Secondly, we solve the
Riemann problem of the Euler equations of isentropic gas dynamics with a double
parameter flux approximation including pressure. Further we rigorously prove
that, as the two-parameter flux perturbation vanishes, any Riemann solution
containing two shock waves tends to a delta shock solution to the zero-pressure
flow; any Riemann solution containing two rarefaction waves tends to a
two-contact-discontinuity solution to the zero-pressure flow and the nonvacuum
intermediate state in between tends to a vacuum state.
