Isotonicity of the Metric Projection and Complementarity Problems in Hilbert Spaces
© 2017 Springer Science+Business Media, LLC 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...
| Main Authors: | , , |
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| Format: | Journal Article |
| Published: |
Springer New York LLC
2017
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| Online Access: | http://hdl.handle.net/20.500.11937/57925 |
| _version_ | 1848760133625053184 |
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| author | Kong, D. Liu, Lishan Wu, Yong Hong |
| author_facet | Kong, D. Liu, Lishan Wu, Yong Hong |
| author_sort | Kong, D. |
| building | Curtin Institutional Repository |
| collection | Online Access |
| description | © 2017 Springer Science+Business Media, LLC 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. |
| first_indexed | 2025-11-14T10:10:56Z |
| format | Journal Article |
| id | curtin-20.500.11937-57925 |
| institution | Curtin University Malaysia |
| institution_category | Local University |
| last_indexed | 2025-11-14T10:10:56Z |
| publishDate | 2017 |
| publisher | Springer New York LLC |
| recordtype | eprints |
| repository_type | Digital Repository |
| spelling | curtin-20.500.11937-579252017-11-20T08:58:33Z Isotonicity of the Metric Projection and Complementarity Problems in Hilbert Spaces Kong, D. Liu, Lishan Wu, Yong Hong © 2017 Springer Science+Business Media, LLC 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. 2017 Journal Article http://hdl.handle.net/20.500.11937/57925 10.1007/s10957-017-1162-8 Springer New York LLC restricted |
| spellingShingle | Kong, D. Liu, Lishan Wu, Yong Hong Isotonicity of the Metric Projection and Complementarity Problems in Hilbert Spaces |
| title | Isotonicity of the Metric Projection and Complementarity Problems in Hilbert Spaces |
| title_full | Isotonicity of the Metric Projection and Complementarity Problems in Hilbert Spaces |
| title_fullStr | Isotonicity of the Metric Projection and Complementarity Problems in Hilbert Spaces |
| title_full_unstemmed | Isotonicity of the Metric Projection and Complementarity Problems in Hilbert Spaces |
| title_short | Isotonicity of the Metric Projection and Complementarity Problems in Hilbert Spaces |
| title_sort | isotonicity of the metric projection and complementarity problems in hilbert spaces |
| url | http://hdl.handle.net/20.500.11937/57925 |