  The effect of competing nonlinearity on beam dynamics in parity-time
$(\mathcal{PT})$ symmetric potentials is investigated. By using numerical
methods, the existence of gap solitons is demonstrated in the first Bragg gap
of optical $\mathcal{PT}$ symmetric lattices with competing nonlinearity.
Meanwhile, the stability of such solitons is analyzed through introducing a
small perturbation to the solitary solutions. The abrupt annihilation of the
solitons during propagation demonstrates the Bragg gap solitons in
$\mathcal{PT}$ symmetric potentials are not stable. In comparison with the
on-site gap solitons, the off-site gap solitons exhibit more robust properties
during propagation.
