Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
842057 | Nonlinear Analysis: Theory, Methods & Applications | 2011 | 6 Pages |
Abstract
This paper gives a solution existence theorem for a generalized variational inequality problem with an operator which is defined on an infinite dimensional space, which is C-pseudomonotone in the sense of Inoan and Kolumbán [D. Inoan, J. Kolumbán, On pseudomonotone set-valued mappings, Nonlinear Analysis 68 (2008) 47–53], but which may not be upper semicontinuous on finite dimensional subspaces. The proof of the theorem provides a new technique which reduces infinite variational inequality problems to finite ones. Two examples are given and analyzed to illustrate the theorem. Moreover, an example is presented to show that the C-pseudomonotonicity of the operator cannot be omitted in the theorem.
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Authors
B.T. Kien, G.M. Lee,