Continuity of Metric Projection Operator from C[0, 1] onto Pn with Applications to Mordukhovich Derivatives
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arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2024
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| _version_ | 1866909384178663424 |
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| author | Li, Jinlu |
| author_facet | Li, Jinlu |
| contents | Let C[0, 1] be the Banach space of all continuous real valued functions on [0, 1]. For an arbitrarily given nonnegative integer n, let Pn denote the set of all polynomials with degree less than or equal to n. Pn is a closed subspace of C[0, 1]. In this paper, we first prove (in details) that the metric projection operator from C[0, 1] to Pn is a single-valued mapping and it is (norm to norm) continuous. Then, we use the continuity of Pn to investigate the Gateaux directional derivatives, some properties and fixed-point properties of the Mordukhovich derivatives of the metric projection operator. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2411_07178 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Continuity of Metric Projection Operator from C[0, 1] onto Pn with Applications to Mordukhovich Derivatives Li, Jinlu Functional Analysis 47H05, 46C05, 49M27, 65K10, 90C25 Let C[0, 1] be the Banach space of all continuous real valued functions on [0, 1]. For an arbitrarily given nonnegative integer n, let Pn denote the set of all polynomials with degree less than or equal to n. Pn is a closed subspace of C[0, 1]. In this paper, we first prove (in details) that the metric projection operator from C[0, 1] to Pn is a single-valued mapping and it is (norm to norm) continuous. Then, we use the continuity of Pn to investigate the Gateaux directional derivatives, some properties and fixed-point properties of the Mordukhovich derivatives of the metric projection operator. |
| title | Continuity of Metric Projection Operator from C[0, 1] onto Pn with Applications to Mordukhovich Derivatives |
| topic | Functional Analysis 47H05, 46C05, 49M27, 65K10, 90C25 |
| url | https://arxiv.org/abs/2411.07178 |