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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2502.00746 |
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| _version_ | 1866915134162599936 |
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| author | Thieu, Nguyen Nang Yen, Nguyen Dong |
| author_facet | Thieu, Nguyen Nang Yen, Nguyen Dong |
| contents | This paper aims at giving solutions to six interesting interconnected open questions suggested by Professor Biagio Ricceri. The questions focus on the behavior of nonvanishing continuous vector-valued functions in finite-dimensional normed spaces as well as in infinite-dimensional normed spaces. Using the celebrated Hartman-Stampacchia Theorem (1966) on the solution existence of variational inequalities, we establish sharp lower estimates for the maximum displacements of nonvanishing continuous vector-valued functions. Then, combining the obtained results with suitable tools from functional analysis and several novel geometrical constructions, we get the above-mentioned solutions. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2502_00746 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | The Hartman-Stampacchia Theorem and the Maximum Displacements of Nonvanishing Continuous Vector-Valued Functions Thieu, Nguyen Nang Yen, Nguyen Dong Functional Analysis This paper aims at giving solutions to six interesting interconnected open questions suggested by Professor Biagio Ricceri. The questions focus on the behavior of nonvanishing continuous vector-valued functions in finite-dimensional normed spaces as well as in infinite-dimensional normed spaces. Using the celebrated Hartman-Stampacchia Theorem (1966) on the solution existence of variational inequalities, we establish sharp lower estimates for the maximum displacements of nonvanishing continuous vector-valued functions. Then, combining the obtained results with suitable tools from functional analysis and several novel geometrical constructions, we get the above-mentioned solutions. |
| title | The Hartman-Stampacchia Theorem and the Maximum Displacements of Nonvanishing Continuous Vector-Valued Functions |
| topic | Functional Analysis |
| url | https://arxiv.org/abs/2502.00746 |