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 $O(1/t)$.

This paper is accepted for publication in Journal of Fixed Point Theory and Applications. arXiv admin note: text overlap with arXiv:1711.01937, and text overlap with arXiv:1507.07302 by other authors