Uniqueness of supporting hyperplanes and an alternative to solutions of variational inequalities |
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| Authors: | Songnian He Hong-Kun Xu |
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| Institution: | 1. College of Science, Civil Aviation University of China, Tianjin, 300300, China
2. Department of Applied Mathematics, National Sun Yat-sen University, Kaohsiung, 80424, Taiwan
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| Abstract: | A uniqueness theorem of supporting hyperplanes for a class of convex level sets in a Hilbert space is obtained. As an application of this result, we prove an alternative theorem on solutions of variational inequalities defined on convex level sets. Three examples are given to demonstrate the usefulness and advantages of our alternative theorem. |
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