Relaxed projection methods for solving variational inequality problems

In this paper, we introduce a new relaxed projection approach for solving the variational inequality problems in a real Hilbert space. First, we propose a solution mapping and show its strongly quasi-nonexpansive properties. Next, we apply the mapping to present two algorithms for solving partially pseudomonotone variational inequality problems and split variational inequality problems. Weak convergence of the algorithms is showed under partially pseudomonotone and Lipschitz continuous assumptions of the cost mappings. Finally, we give some numerical results for the proposed algorithms and comparison with other known methods.