  We propose a novel two-dimensional (2D)frustrated quantum spin-1/2
anisotropic Heisenberg model with alternating ferromagnetic and
antiferromagnetic magnetic chains along one direction and antiferromagnetic
interactions along the other. The (mean-field) ground state is ferrimagnetic in
certain range of the interaction space. Spin-wave theory analysis of the
reduction of ordered moments at inequivalent spin sites and the instability of
the spin waves suggest a quantum phase transition which has the characteristics
of both the frustrated two-dimensional antiferromagnetic S=1/2 ($J_1, J_2$)
model and 1D S$_1$=1, S$_2$=1/2 quantum ferrimagnetic model.
