In this paper we introduce an iterative process to find a common element of the set of fixed points of a strict pseudo-contraction and the set of solutions of the variational inequality problem for a monotone and Lipschitz continuous mapping. The iterative process is based on the so-called modified extragradient method. We obtain a weak convergence theorem for two sequences generated by this process. Using this theorem, we also construct an iterative process to find a common element of the set of fixed points of a strict pseudo-contraction and the set of zeroes of a monotone and Lipschitz continuous mapping.
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