On a New Geometric Constant Related to the Euler-Lagrange Type Identity in Banach Spaces
In this paper, we will introduce a new geometric constant <inline-formula><math display="inline"><semantics><mrow><msub><mi>L</mi><mi>YJ</mi></msub><mrow><mo>(</mo><mi>λ</mi><mo>,</mo><...
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| Language: | English |
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MDPI AG
2021-01-01
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| Series: | Mathematics |
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| Online Access: | https://www.mdpi.com/2227-7390/9/2/116 |
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| author | Qi Liu Yongjin Li |
| author_facet | Qi Liu Yongjin Li |
| author_sort | Qi Liu |
| collection | DOAJ |
| description | In this paper, we will introduce a new geometric constant <inline-formula><math display="inline"><semantics><mrow><msub><mi>L</mi><mi>YJ</mi></msub><mrow><mo>(</mo><mi>λ</mi><mo>,</mo><mi>μ</mi><mo>,</mo><mi>X</mi><mo>)</mo></mrow></mrow></semantics></math></inline-formula> based on an equivalent characterization of inner product space, which was proposed by Moslehian and Rassias. We first discuss some equivalent forms of the proposed constant. Next, a characterization of uniformly non-square is given. Moreover, some sufficient conditions which imply weak normal structure are presented. Finally, we obtain some relationship between the other well-known geometric constants and <inline-formula><math display="inline"><semantics><mrow><msub><mi>L</mi><mi>YJ</mi></msub><mrow><mo>(</mo><mi>λ</mi><mo>,</mo><mi>μ</mi><mo>,</mo><mi>X</mi><mo>)</mo></mrow></mrow></semantics></math></inline-formula>. Also, this new coefficient is computed for <i>X</i> being concrete space. |
| first_indexed | 2024-03-09T05:51:20Z |
| format | Article |
| id | doaj.art-804e4bd8211748c9801a57404624dc0d |
| institution | Directory Open Access Journal |
| issn | 2227-7390 |
| language | English |
| last_indexed | 2024-03-09T05:51:20Z |
| publishDate | 2021-01-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Mathematics |
| spelling | doaj.art-804e4bd8211748c9801a57404624dc0d2023-12-03T12:17:14ZengMDPI AGMathematics2227-73902021-01-019211610.3390/math9020116On a New Geometric Constant Related to the Euler-Lagrange Type Identity in Banach SpacesQi Liu0Yongjin Li1School of Mathematics, Sun Yat-Sen University, Guangzhou 510275, ChinaSchool of Mathematics, Sun Yat-Sen University, Guangzhou 510275, ChinaIn this paper, we will introduce a new geometric constant <inline-formula><math display="inline"><semantics><mrow><msub><mi>L</mi><mi>YJ</mi></msub><mrow><mo>(</mo><mi>λ</mi><mo>,</mo><mi>μ</mi><mo>,</mo><mi>X</mi><mo>)</mo></mrow></mrow></semantics></math></inline-formula> based on an equivalent characterization of inner product space, which was proposed by Moslehian and Rassias. We first discuss some equivalent forms of the proposed constant. Next, a characterization of uniformly non-square is given. Moreover, some sufficient conditions which imply weak normal structure are presented. Finally, we obtain some relationship between the other well-known geometric constants and <inline-formula><math display="inline"><semantics><mrow><msub><mi>L</mi><mi>YJ</mi></msub><mrow><mo>(</mo><mi>λ</mi><mo>,</mo><mi>μ</mi><mo>,</mo><mi>X</mi><mo>)</mo></mrow></mrow></semantics></math></inline-formula>. Also, this new coefficient is computed for <i>X</i> being concrete space.https://www.mdpi.com/2227-7390/9/2/116uniformly non-square Banach spacevon Neumann–Jordan constantEuler-Lagrange type identity |
| spellingShingle | Qi Liu Yongjin Li On a New Geometric Constant Related to the Euler-Lagrange Type Identity in Banach Spaces Mathematics uniformly non-square Banach space von Neumann–Jordan constant Euler-Lagrange type identity |
| title | On a New Geometric Constant Related to the Euler-Lagrange Type Identity in Banach Spaces |
| title_full | On a New Geometric Constant Related to the Euler-Lagrange Type Identity in Banach Spaces |
| title_fullStr | On a New Geometric Constant Related to the Euler-Lagrange Type Identity in Banach Spaces |
| title_full_unstemmed | On a New Geometric Constant Related to the Euler-Lagrange Type Identity in Banach Spaces |
| title_short | On a New Geometric Constant Related to the Euler-Lagrange Type Identity in Banach Spaces |
| title_sort | on a new geometric constant related to the euler lagrange type identity in banach spaces |
| topic | uniformly non-square Banach space von Neumann–Jordan constant Euler-Lagrange type identity |
| url | https://www.mdpi.com/2227-7390/9/2/116 |
| work_keys_str_mv | AT qiliu onanewgeometricconstantrelatedtotheeulerlagrangetypeidentityinbanachspaces AT yongjinli onanewgeometricconstantrelatedtotheeulerlagrangetypeidentityinbanachspaces |