Orlicz Mean Dual Affine Quermassintegrals
Our main aim is to generalize the mean dual affine quermassintegrals to the Orlicz space. Under the framework of dual Orlicz-Brunn-Minkowski theory, we introduce a new affine geometric quantity by calculating the first Orlicz variation of the mean dual affine quermassintegrals and call it the Orlicz...
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| Format: | Article |
| Language: | English |
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Wiley
2018-01-01
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| Series: | Journal of Function Spaces |
| Online Access: | http://dx.doi.org/10.1155/2018/8123924 |
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| author | Chang-Jian Zhao Wing-Sum Cheung |
| author_facet | Chang-Jian Zhao Wing-Sum Cheung |
| author_sort | Chang-Jian Zhao |
| collection | DOAJ |
| description | Our main aim is to generalize the mean dual affine quermassintegrals to the Orlicz space. Under the framework of dual Orlicz-Brunn-Minkowski theory, we introduce a new affine geometric quantity by calculating the first Orlicz variation of the mean dual affine quermassintegrals and call it the Orlicz mean dual affine quermassintegral. The fundamental notions and conclusions of the mean dual affine quermassintegrals and the Minkowski and Brunn-Minkowski inequalities for them are extended to an Orlicz setting. The related concepts and inequalities of dual Orlicz mixed volumes are also included in our conclusions. The new Orlicz isoperimetric inequalities in special case yield the Lp-dual Minkowski inequality and Brunn-Minkowski inequality for the mean dual affine quermassintegrals, which also imply the dual Orlicz-Minkowski inequality and dual Orlicz-Brunn-Minkowski inequality. |
| format | Article |
| id | doaj-art-6e5600679b5647fbbd3c92ada1e887f2 |
| institution | Kabale University |
| issn | 2314-8896 2314-8888 |
| language | English |
| publishDate | 2018-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Function Spaces |
| spelling | doaj-art-6e5600679b5647fbbd3c92ada1e887f22025-02-03T05:58:53ZengWileyJournal of Function Spaces2314-88962314-88882018-01-01201810.1155/2018/81239248123924Orlicz Mean Dual Affine QuermassintegralsChang-Jian Zhao0Wing-Sum Cheung1Department of Mathematics, China Jiliang University, Hangzhou 310018, ChinaDepartment of Mathematics, The University of Hong Kong, Pokfulam Road, Pokfulam, Hong KongOur main aim is to generalize the mean dual affine quermassintegrals to the Orlicz space. Under the framework of dual Orlicz-Brunn-Minkowski theory, we introduce a new affine geometric quantity by calculating the first Orlicz variation of the mean dual affine quermassintegrals and call it the Orlicz mean dual affine quermassintegral. The fundamental notions and conclusions of the mean dual affine quermassintegrals and the Minkowski and Brunn-Minkowski inequalities for them are extended to an Orlicz setting. The related concepts and inequalities of dual Orlicz mixed volumes are also included in our conclusions. The new Orlicz isoperimetric inequalities in special case yield the Lp-dual Minkowski inequality and Brunn-Minkowski inequality for the mean dual affine quermassintegrals, which also imply the dual Orlicz-Minkowski inequality and dual Orlicz-Brunn-Minkowski inequality.http://dx.doi.org/10.1155/2018/8123924 |
| spellingShingle | Chang-Jian Zhao Wing-Sum Cheung Orlicz Mean Dual Affine Quermassintegrals Journal of Function Spaces |
| title | Orlicz Mean Dual Affine Quermassintegrals |
| title_full | Orlicz Mean Dual Affine Quermassintegrals |
| title_fullStr | Orlicz Mean Dual Affine Quermassintegrals |
| title_full_unstemmed | Orlicz Mean Dual Affine Quermassintegrals |
| title_short | Orlicz Mean Dual Affine Quermassintegrals |
| title_sort | orlicz mean dual affine quermassintegrals |
| url | http://dx.doi.org/10.1155/2018/8123924 |
| work_keys_str_mv | AT changjianzhao orliczmeandualaffinequermassintegrals AT wingsumcheung orliczmeandualaffinequermassintegrals |