On the solution existence of pseudomonotone variational inequalities |
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Authors: | B. T. Kien J.-C. Yao N. D. Yen |
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Affiliation: | (1) Department of Applied Mathematics, National Sun Yat-Sen University, Kaohsiung, 804, Taiwan;(2) Institute of Mathematics, Vietnamese Academy of Science and Technology, 18 Hoang Quoc Viet, Hanoi, 10307, Vietnam |
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Abstract: | As shown by Thanh Hao [Acta Math. Vietnam 31, 283–289, 2006], the solution existence results established by Facchinei and Pang [Finite-Dimensional Variational Inequalities and Complementarity Problems, vol. I (Springer, Berlin, 2003) Prop. 2.2.3 and Theorem 2.3.4] for variational inequalities (VIs) in general and for pseudomonotone VIs in particular, are very useful for studying the range of applicability of the Tikhonov regularization method. This paper proposes some extensions of these results of Facchinei and Pang to the case of generalized variational inequalities (GVI) and of variational inequalities in infinite-dimensional reflexive Banach spaces. Various examples are given to analyze in detail the obtained results. B. T. Kien: On leave from Hanoi University of Civil Engineering. The online version of the original article can be found at . |
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Keywords: | Variational inequality Generalized variational inequality Pseudomonotone operator Solution existence Degree theory |
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