  In this paper we study the bounded perturbation resilience of projection and
contraction algorithms for solving variational inequality (VI) problems in real
Hilbert spaces. Under typical and standard assumptions of monotonicity and
Lipschitz continuity of the VI's associated mapping, convergence of the
perturbed projection and contraction algorithms is proved. Based on the bounded
perturbed resilience of projection and contraction algorithms, we present some
inertial projection and contraction algorithms. In addition we show that the
perturbed algorithms converges at the rate of $O(1/t)$.
