Characterization of the Cone and Applications in Banach Spaces |
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| Authors: | Dezhou Kong Yonghong Wu |
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| Affiliation: | 1. College of Information Science and Engineering, Shandong Agricultural University, Taian, Shandong, China;2. School of Mathematical Sciences, Qufu Normal University, Qufu, Shandong, China;3. Department of Mathematics and Statistics, Curtin University, Perth, Western Australia, Australia |
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| Abstract: | AbstractIn this article, we first discuss the subduality and orthogonality of the cones and the dual cones when the norm is monotone in Banach spaces. Then, under different assumptions, the necessary and sufficient conditions for the ordering increasing property of the metric projection onto cones and order intervals are studied. Moreover, representations of the metric projection onto cones and order intervals are obtained. As applications, the solvability and approximation results of solutions to nonlinear discontinuous variational inequality and complementarity problems are proved by partial ordering methods. |
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| Keywords: | Cone Banach spaces metric projection variational inequality complementarity problem |
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