  The d-wave superconductivity (dSC) and antiferromagnetism are analytically
studied in a renormalized mean field theory for a two dimensional t-J model
plus an on-site repulsive Hubbard interaction $U$. The purpose of introducing
the $U$ term is to partially impose the no double occupancy constraint by
employing the Gutzwiller approximation. The phase diagrams as functions of
doping $\delta$ and $U$ are studied. Using the standard value of $t/J=3.0$ and
in the large $U$ limit, we show that the antiferromagnetic (AF) order emerges
and coexists with the dSC in the underdoped region below the doping
$\delta\sim0.1$. The dSC order parameter increases from zero as the doping
increases and reaches a maximum near the optimal doping $\delta\sim0.15$. In
the small $U$ limit, only the dSC order survives while the AF order disappears.
As $U$ increased to a critical value, the AF order shows up and coexists with
the dSC in the underdoped regime. At half filing, the system is in the dSC
state for small $U$ and becomes an AF insulator for large $U$. Within the
present mean field approach, We show that the ground state energy of the
coexistent state is always lower than that of the pure dSC state.
