On the Metric Projection Operator and Its Applications to Solving Variational Inequalities in Banach Spaces |
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| Authors: | Jinlu Li Congjun Zhang Xinhua Ma |
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| Institution: | 1. Department of Mathematical Sciences , Shawnee State University , Portsmouth, Ohio, USA jli@shawnee.edu;3. Department of Applied Mathematics , Nanjing Economics and Finance University , Nanjing, Jiangsu, China;4. College of Science , Hebei Polytechnic University , Tangshan, Hebei, China |
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| Abstract: | In this paper, we investigate the characteristics of the metric projection operator P K : B → K, where B is a Banach space with dual space B?, and K is a nonempty closed convex subset of B. Then we apply its properties to study the existence of solutions of variational inequalities in uniformly convex and uniformly smooth Banach spaces. |
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| Keywords: | Fixed point Leray-Schauder type alternative theorem Metric projection operator Variational inequality |
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