Functional inequalities in the framework of Banach spaces
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arXiv
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866909287340572672 |
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| author | Niculescu, Constantin P. |
| author_facet | Niculescu, Constantin P. |
| contents | A quadrilateral inequality established by C. Schötz in the context of Hilbert spaces is extended to the framework of Banach spaces. Our approach is based on the majorization theory and a substitute for the parallelogram law associated with Clarkson's notion of von Neumann-Jordan constant. As a by-product, several functional inequalities that extend classical inequalities from linear algebra and geometry of Banach spaces are also obtained. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2405_20097 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Functional inequalities in the framework of Banach spaces Niculescu, Constantin P. Functional Analysis Classical Analysis and ODEs 26A51, 39B62, 46B20 A quadrilateral inequality established by C. Schötz in the context of Hilbert spaces is extended to the framework of Banach spaces. Our approach is based on the majorization theory and a substitute for the parallelogram law associated with Clarkson's notion of von Neumann-Jordan constant. As a by-product, several functional inequalities that extend classical inequalities from linear algebra and geometry of Banach spaces are also obtained. |
| title | Functional inequalities in the framework of Banach spaces |
| topic | Functional Analysis Classical Analysis and ODEs 26A51, 39B62, 46B20 |
| url | https://arxiv.org/abs/2405.20097 |