A projection-type method for generalized variational inequalities with dual solutions
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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.
Share and Cite
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
Keywords
- Projection method
- generalized variational inequality
- dual variational inequality.
MSC
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