Isotonicity of the Metric Projection and Complementarity Problems in Hilbert Spaces |
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Authors: | Dezhou Kong Lishan Liu Yonghong Wu |
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Institution: | 1.College of Information Science and Engineering,Shandong Agricultural University,Taian,China;2.School of Mathematical Sciences,Qufu Normal University,Qufu,China;3.Department of Mathematics and Statistics,Curtin University,Perth,Australia |
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Abstract: | In this paper, as the extension of the isotonicity of the metric projection, the isotonicity characterizations with respect to two arbitrary order relations induced by cones of the metric projection operator are studied in Hilbert spaces, when one cone is a subdual cone and some relations between the two orders hold. Moreover, if the metric projection is not isotone in the whole space, we prove that the metric projection is isotone in some domains in both Hilbert lattices and Hilbert quasi-lattices. By using the isotonicity characterizations with respect to two arbitrary order relations of the metric projection, some solvability and approximation theorems for the complementarity problems are obtained. Our results generalize and improve various recent results in the field of study. |
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