Frechet and Mordukhovich Derivative (Coderivative) and Covering Constant for Single-Valued Mapping in Euclidean Space with Application (II)
Fuente:
arXiv
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866915451095744512 |
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| author | Li, Jinlu |
| author_facet | Li, Jinlu |
| contents | We continue the study in part I for calculating the Frechet derivatives and Mordukhovich derivatives (coderivatives) and covering constants for single-valued mappings in Euclidean spaces (It is part I). In this paper, we particularly consider a norm-reserved mapping f: R^2 to R^2 that is defined by (1.1) in Section 1. We will find the precise solutions of Frechet derivative and Mordukhovich derivative at every point in R^2. By using these solutions, we will find the covering constant for this mapping f is exact 1 at every point in R^2 except the origin. Then we extend this mapping to R^4. Finally, by using the covering constant for f and by applying the Arutyunov Mordukhovich and Zhukovskiy Parameterized Coincidence Point Theorem, we will solve some parameterized equations. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2508_11118 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Frechet and Mordukhovich Derivative (Coderivative) and Covering Constant for Single-Valued Mapping in Euclidean Space with Application (II) Li, Jinlu Functional Analysis 49J52, 49J53, 47H10, 90C31 We continue the study in part I for calculating the Frechet derivatives and Mordukhovich derivatives (coderivatives) and covering constants for single-valued mappings in Euclidean spaces (It is part I). In this paper, we particularly consider a norm-reserved mapping f: R^2 to R^2 that is defined by (1.1) in Section 1. We will find the precise solutions of Frechet derivative and Mordukhovich derivative at every point in R^2. By using these solutions, we will find the covering constant for this mapping f is exact 1 at every point in R^2 except the origin. Then we extend this mapping to R^4. Finally, by using the covering constant for f and by applying the Arutyunov Mordukhovich and Zhukovskiy Parameterized Coincidence Point Theorem, we will solve some parameterized equations. |
| title | Frechet and Mordukhovich Derivative (Coderivative) and Covering Constant for Single-Valued Mapping in Euclidean Space with Application (II) |
| topic | Functional Analysis 49J52, 49J53, 47H10, 90C31 |
| url | https://arxiv.org/abs/2508.11118 |