A new constant in Banach spaces based on the Zb$ \check{a} $ganu constant $ C_{Z}(B) $
In Banach spaces, first we present a new geometric constant, $ C_{Z}^{(q)}(t, B) $, which is closely related to the Zb$ \check{a} $ganu constant. We prove that $ \frac{(t+2)^{q}}{2^{q-1}\left(2^{q-1}+t^{q}\right)} $ and $ \frac{4}{3} $ are respectively the lower and upper bounds for $ C_{Z}^{(q)}(t,...
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| Language: | English |
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AIMS Press
2025-03-01
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| Series: | AIMS Mathematics |
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| Online Access: | https://www.aimspress.com/article/doi/10.3934/math.2025296 |
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| author | Qian Li Zhouping Yin Yuxin Wang Qi Liu Hongmei Zhang |
| author_facet | Qian Li Zhouping Yin Yuxin Wang Qi Liu Hongmei Zhang |
| author_sort | Qian Li |
| collection | DOAJ |
| description | In Banach spaces, first we present a new geometric constant, $ C_{Z}^{(q)}(t, B) $, which is closely related to the Zb$ \check{a} $ganu constant. We prove that $ \frac{(t+2)^{q}}{2^{q-1}\left(2^{q-1}+t^{q}\right)} $ and $ \frac{4}{3} $ are respectively the lower and upper bounds for $ C_{Z}^{(q)}(t, B) $. Furthermore, we also derive that $ C_{Z}^{(q)}(t, B) = C_{Z}^{(q)}(t, \widetilde{B}) $, where $ \widetilde{B} $ denotes the ultrapower spaces of $ B $. Then, we can establish certain sufficient conditions that ensure a Banach spaces possesses a normal structure, which involve different constants such as the Zb$ \check{a} $ganu constant and Domínguez–Benavides coefficient. |
| format | Article |
| id | doaj-art-ce58b063248446d78a30aebac76e26ec |
| institution | OA Journals |
| issn | 2473-6988 |
| language | English |
| publishDate | 2025-03-01 |
| publisher | AIMS Press |
| record_format | Article |
| series | AIMS Mathematics |
| spelling | doaj-art-ce58b063248446d78a30aebac76e26ec2025-08-20T02:08:20ZengAIMS PressAIMS Mathematics2473-69882025-03-011036480649110.3934/math.2025296A new constant in Banach spaces based on the Zb$ \check{a} $ganu constant $ C_{Z}(B) $Qian Li0Zhouping Yin1Yuxin Wang2Qi Liu3Hongmei Zhang4School of Mathematics and Physics, Anqing Normal University, Anqing 246133, ChinaSchool of Mathematics and Physics, Anqing Normal University, Anqing 246133, ChinaSchool of Mathematics and Physics, Anqing Normal University, Anqing 246133, ChinaSchool of Mathematics and Physics, Anqing Normal University, Anqing 246133, ChinaSchool of Mathematics and Physics, Anqing Normal University, Anqing 246133, ChinaIn Banach spaces, first we present a new geometric constant, $ C_{Z}^{(q)}(t, B) $, which is closely related to the Zb$ \check{a} $ganu constant. We prove that $ \frac{(t+2)^{q}}{2^{q-1}\left(2^{q-1}+t^{q}\right)} $ and $ \frac{4}{3} $ are respectively the lower and upper bounds for $ C_{Z}^{(q)}(t, B) $. Furthermore, we also derive that $ C_{Z}^{(q)}(t, B) = C_{Z}^{(q)}(t, \widetilde{B}) $, where $ \widetilde{B} $ denotes the ultrapower spaces of $ B $. Then, we can establish certain sufficient conditions that ensure a Banach spaces possesses a normal structure, which involve different constants such as the Zb$ \check{a} $ganu constant and Domínguez–Benavides coefficient.https://www.aimspress.com/article/doi/10.3934/math.2025296geometric constantsbanach spacezb$ \check{a} $ganu constantultrapower spacenormal structure |
| spellingShingle | Qian Li Zhouping Yin Yuxin Wang Qi Liu Hongmei Zhang A new constant in Banach spaces based on the Zb$ \check{a} $ganu constant $ C_{Z}(B) $ AIMS Mathematics geometric constants banach space zb$ \check{a} $ganu constant ultrapower space normal structure |
| title | A new constant in Banach spaces based on the Zb$ \check{a} $ganu constant $ C_{Z}(B) $ |
| title_full | A new constant in Banach spaces based on the Zb$ \check{a} $ganu constant $ C_{Z}(B) $ |
| title_fullStr | A new constant in Banach spaces based on the Zb$ \check{a} $ganu constant $ C_{Z}(B) $ |
| title_full_unstemmed | A new constant in Banach spaces based on the Zb$ \check{a} $ganu constant $ C_{Z}(B) $ |
| title_short | A new constant in Banach spaces based on the Zb$ \check{a} $ganu constant $ C_{Z}(B) $ |
| title_sort | new constant in banach spaces based on the zb check a ganu constant c z b |
| topic | geometric constants banach space zb$ \check{a} $ganu constant ultrapower space normal structure |
| url | https://www.aimspress.com/article/doi/10.3934/math.2025296 |
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