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In this paper, some new accelerated iterative schemes are proposed to solve the variational inequality problem with a pseudomonotone and uniformly continuous operator in real Hilbert spaces. Strong convergence theorems of the suggested algorithms are obtained without the prior knowledge of the Lipschitz constant of the operator. Some numerical experiments and applications are performed to illustrate the advantages of the proposed methods with respect to several related ones.

Inertial projection and contraction methods for pseudomonotone variational inequalities with non-Lipschitz operators and applications