Bulletin of the Korean Mathematical Society (대한수학회보)
- Volume 28 Issue 2
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- Pages.163-174
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- 1991
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- 1015-8634(pISSN)
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- 2234-3016(eISSN)
REMARKS ON SOME VARIATIONAL INEQUALITIES
Abstract
This is a continuation of the author's previous work [17]. In this paper, we consider mainly variational inequalities for single-valued functions. We first obtain a generalization of the variational type inequality of Juberg and Karamardian [10] and apply it to obtain strengthened versions of the Hartman-Stampacchia inequality and the Brouwer fixed point theorem. Next, we obtain fairly general versions of Browder's variational inequality [5] and its subsequent generalizations due to Brezis et al [4], Takahashk [23], Shih and Tan [19], Simons [20], and others. Finally, in this paper, we obtain a variational inequality for non-real locally convex t.v.s. which generalizes a result of Shih and Tan [19].
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