A projection-type method for generalized variational inequalities with dual solutions

In this paper, a new projection-type method for generalized variational inequalities is introduced in Euclidean spaces. Under the assumption that the dual variational inequality has a solution, we show that the proposed method is well-defined and prove that the sequence generated by the proposed method is convergent to a solution, where the condition is strictly weaker than the pseudomonotonicity of the mapping used by some authors. We provide an example to support our results. Compared with the recent works of Li and He [F.-L. Li, Y.-R. He, J. Comput. Appl. Math., 228 (2009), 212–218], and Fang and He [C.-J. Fang, Y.-R. He, Appl. Math. Comput., 217 (2011), 9543–9551], condition (A3) is removed. Moreover, the results presented in this paper also generalize and improve some known results given in other literature.