Relations between generalized von Neumann-Jordan and James constants for quasi-Banach spaces
Abstract Let C N J ( B ) $\mathcal{C}_{NJ} ( \mathcal{B} )$ and J ( B ) $J ( \mathcal{B} )$ be the generalized von Neumann-Jordan and James constants of a quasi-Banach space B $\mathcal{B}$ , respectively. In this paper we shall show the relation between C N J ( B ) $\mathcal {C}_{NJ} ( \mathcal{B}...
| Main Authors: | , , , , |
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| Format: | Article |
| Language: | English |
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SpringerOpen
2016-07-01
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| Series: | Journal of Inequalities and Applications |
| Subjects: | |
| Online Access: | http://link.springer.com/article/10.1186/s13660-016-1115-z |
| _version_ | 1828909103914680320 |
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| author | Young Chel Kwun Qaisar Mehmood Waqas Nazeer Absar Ul Haq Shin Min Kang |
| author_facet | Young Chel Kwun Qaisar Mehmood Waqas Nazeer Absar Ul Haq Shin Min Kang |
| author_sort | Young Chel Kwun |
| collection | DOAJ |
| description | Abstract Let C N J ( B ) $\mathcal{C}_{NJ} ( \mathcal{B} )$ and J ( B ) $J ( \mathcal{B} )$ be the generalized von Neumann-Jordan and James constants of a quasi-Banach space B $\mathcal{B}$ , respectively. In this paper we shall show the relation between C N J ( B ) $\mathcal {C}_{NJ} ( \mathcal{B} )$ , J ( B ) $J ( \mathcal{B} )$ , and the modulus of convexity. Also, we show that if B $\mathcal{B}$ is not uniform non-square then J ( B ) = C N J ( B ) = 2 $J ( \mathcal{B} )=\mathcal{C}_{NJ} ( \mathcal{B} )=2$ . Moreover, we give an equivalent formula for the generalized von Neumann-Jordan constant. |
| first_indexed | 2024-12-13T18:21:29Z |
| format | Article |
| id | doaj.art-3a13afce24ea439fa2dcbaf7cf3f3884 |
| institution | Directory Open Access Journal |
| issn | 1029-242X |
| language | English |
| last_indexed | 2024-12-13T18:21:29Z |
| publishDate | 2016-07-01 |
| publisher | SpringerOpen |
| record_format | Article |
| series | Journal of Inequalities and Applications |
| spelling | doaj.art-3a13afce24ea439fa2dcbaf7cf3f38842022-12-21T23:35:42ZengSpringerOpenJournal of Inequalities and Applications1029-242X2016-07-012016111010.1186/s13660-016-1115-zRelations between generalized von Neumann-Jordan and James constants for quasi-Banach spacesYoung Chel Kwun0Qaisar Mehmood1Waqas Nazeer2Absar Ul Haq3Shin Min Kang4Department of Mathematics, Dong-A UniversityDepartment of Mathematics, Science CollegeDivision of Science and Technology, University of EducationAbdus Salam School of Mathmatical Sciences, GC UniversityDepartment of Mathematics and RINS, Gyeongsang National UniversityAbstract Let C N J ( B ) $\mathcal{C}_{NJ} ( \mathcal{B} )$ and J ( B ) $J ( \mathcal{B} )$ be the generalized von Neumann-Jordan and James constants of a quasi-Banach space B $\mathcal{B}$ , respectively. In this paper we shall show the relation between C N J ( B ) $\mathcal {C}_{NJ} ( \mathcal{B} )$ , J ( B ) $J ( \mathcal{B} )$ , and the modulus of convexity. Also, we show that if B $\mathcal{B}$ is not uniform non-square then J ( B ) = C N J ( B ) = 2 $J ( \mathcal{B} )=\mathcal{C}_{NJ} ( \mathcal{B} )=2$ . Moreover, we give an equivalent formula for the generalized von Neumann-Jordan constant.http://link.springer.com/article/10.1186/s13660-016-1115-zthe generalized von Neumann-Jordan constantJames constantuniform non-squarenessquasi-normed spaces |
| spellingShingle | Young Chel Kwun Qaisar Mehmood Waqas Nazeer Absar Ul Haq Shin Min Kang Relations between generalized von Neumann-Jordan and James constants for quasi-Banach spaces Journal of Inequalities and Applications the generalized von Neumann-Jordan constant James constant uniform non-squareness quasi-normed spaces |
| title | Relations between generalized von Neumann-Jordan and James constants for quasi-Banach spaces |
| title_full | Relations between generalized von Neumann-Jordan and James constants for quasi-Banach spaces |
| title_fullStr | Relations between generalized von Neumann-Jordan and James constants for quasi-Banach spaces |
| title_full_unstemmed | Relations between generalized von Neumann-Jordan and James constants for quasi-Banach spaces |
| title_short | Relations between generalized von Neumann-Jordan and James constants for quasi-Banach spaces |
| title_sort | relations between generalized von neumann jordan and james constants for quasi banach spaces |
| topic | the generalized von Neumann-Jordan constant James constant uniform non-squareness quasi-normed spaces |
| url | http://link.springer.com/article/10.1186/s13660-016-1115-z |
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