Some aspects of generalized Zbăganu and James constant in Banach spaces
We shall introduce a new geometric constant CZ(λ,μ,X){C}_{Z}\left(\lambda ,\mu ,X) based on a generalization of the parallelogram law, which was proposed by Moslehian and Rassias. First, it is shown that, for a Banach space, CZ(λ,μ,X){C}_{Z}\left(\lambda ,\mu ,X) is equal to 1 if and only if the nor...
| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
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De Gruyter
2021-08-01
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| Series: | Demonstratio Mathematica |
| Subjects: | |
| Online Access: | https://doi.org/10.1515/dema-2021-0033 |
| _version_ | 1819001727925354496 |
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| author | Liu Qi Sarfraz Muhammad Li Yongjin |
| author_facet | Liu Qi Sarfraz Muhammad Li Yongjin |
| author_sort | Liu Qi |
| collection | DOAJ |
| description | We shall introduce a new geometric constant CZ(λ,μ,X){C}_{Z}\left(\lambda ,\mu ,X) based on a generalization of the parallelogram law, which was proposed by Moslehian and Rassias. First, it is shown that, for a Banach space, CZ(λ,μ,X){C}_{Z}\left(\lambda ,\mu ,X) is equal to 1 if and only if the norm is induced by an inner product. Next, a characterization of uniformly non-square is given, that is, XX has the fixed point property. Also, a sufficient condition which implies weak normal structure is presented. Moreover, a generalized James constant J(λ,X)J\left(\lambda ,X) is also introduced. Finally, some basic properties of this new coefficient are presented. |
| first_indexed | 2024-12-20T22:53:49Z |
| format | Article |
| id | doaj.art-2d0a85394b5747cca36c18d5877f811d |
| institution | Directory Open Access Journal |
| issn | 2391-4661 |
| language | English |
| last_indexed | 2024-12-20T22:53:49Z |
| publishDate | 2021-08-01 |
| publisher | De Gruyter |
| record_format | Article |
| series | Demonstratio Mathematica |
| spelling | doaj.art-2d0a85394b5747cca36c18d5877f811d2022-12-21T19:24:10ZengDe GruyterDemonstratio Mathematica2391-46612021-08-0154129931010.1515/dema-2021-0033Some aspects of generalized Zbăganu and James constant in Banach spacesLiu Qi0Sarfraz Muhammad1Li Yongjin2Department of Mathematics, Sun Yat-sen University, Guangzhou, 510275, P. R. ChinaDepartment of Mathematics, Sun Yat-sen University, Guangzhou, 510275, P. R. ChinaDepartment of Mathematics, Sun Yat-sen University, Guangzhou, 510275, P. R. ChinaWe shall introduce a new geometric constant CZ(λ,μ,X){C}_{Z}\left(\lambda ,\mu ,X) based on a generalization of the parallelogram law, which was proposed by Moslehian and Rassias. First, it is shown that, for a Banach space, CZ(λ,μ,X){C}_{Z}\left(\lambda ,\mu ,X) is equal to 1 if and only if the norm is induced by an inner product. Next, a characterization of uniformly non-square is given, that is, XX has the fixed point property. Also, a sufficient condition which implies weak normal structure is presented. Moreover, a generalized James constant J(λ,X)J\left(\lambda ,X) is also introduced. Finally, some basic properties of this new coefficient are presented.https://doi.org/10.1515/dema-2021-0033banach spacesgeometric constantsweak normal structureeuler-lagrange identity46b20 |
| spellingShingle | Liu Qi Sarfraz Muhammad Li Yongjin Some aspects of generalized Zbăganu and James constant in Banach spaces Demonstratio Mathematica banach spaces geometric constants weak normal structure euler-lagrange identity 46b20 |
| title | Some aspects of generalized Zbăganu and James constant in Banach spaces |
| title_full | Some aspects of generalized Zbăganu and James constant in Banach spaces |
| title_fullStr | Some aspects of generalized Zbăganu and James constant in Banach spaces |
| title_full_unstemmed | Some aspects of generalized Zbăganu and James constant in Banach spaces |
| title_short | Some aspects of generalized Zbăganu and James constant in Banach spaces |
| title_sort | some aspects of generalized zbaganu and james constant in banach spaces |
| topic | banach spaces geometric constants weak normal structure euler-lagrange identity 46b20 |
| url | https://doi.org/10.1515/dema-2021-0033 |
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