In this paper, we give a new variant of parallel extragradient methods for finding a common element of the solution set of variational inequalities and the fixed point set of a quasi-nonexpansive mapping with a demicloseness property in a real Hilbert space. We present a scheme that combines the idea of the Halpern subgradient extragradient method and parallel computation techniques as a hybrid variant. Then, this scheme is modified by projecting on a suitable convex set to get strong convergence property under certain assumptions of cost mappings.

variational inequalities, fixed point, pseudomonotone, Lipschitz continuous, extragradient method, quasi-nonexpansive mapping.