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


Authors

Ming Zhu - School of Science, Guangxi University for Nationalities, Nanning, Guangxi 530006, P. R. China. Guo-Ji Tang - School of Science, Guangxi University for Nationalities, Nanning, Guangxi 530006, P. R. China.


Abstract

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., \({\bf 228}\) (2009), 212--218], and Fang and He [C.-J. Fang, Y.-R. He, Appl. Math. Comput., \({\bf 217}\) (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.


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ISRP Style

Ming Zhu, Guo-Ji Tang, A projection-type method for generalized variational inequalities with dual solutions, Journal of Nonlinear Sciences and Applications, 10 (2017), no. 9, 4812--4821

AMA Style

Zhu Ming, Tang Guo-Ji, A projection-type method for generalized variational inequalities with dual solutions. J. Nonlinear Sci. Appl. (2017); 10(9):4812--4821

Chicago/Turabian Style

Zhu, Ming, Tang, Guo-Ji. "A projection-type method for generalized variational inequalities with dual solutions." Journal of Nonlinear Sciences and Applications, 10, no. 9 (2017): 4812--4821


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