Non-linear resolvents of holomorphically accretive mappings
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arXiv
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866910472571191296 |
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| author | Elin, Mark |
| author_facet | Elin, Mark |
| contents | In this paper, we present new results on holomorphically accretive mappings and their resolvents defined on the open unit ball of a complex Banach space.
We employ a unified approach to examine various properties of non-linear resolvents by applying a distortion theorem we have established. This method enables us to prove a covering result and to establish the accretivity of resolvents along with estimates of the squeezing ratio. Furthermore, we prove that under certain mild conditions, a non-linear resolvent is a starlike mapping of a specified order.
As a key tool, we first introduce a refined version of the inverse function theorem for mappings satisfying so-called one-sided estimates. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2406_02758 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Non-linear resolvents of holomorphically accretive mappings Elin, Mark Complex Variables In this paper, we present new results on holomorphically accretive mappings and their resolvents defined on the open unit ball of a complex Banach space. We employ a unified approach to examine various properties of non-linear resolvents by applying a distortion theorem we have established. This method enables us to prove a covering result and to establish the accretivity of resolvents along with estimates of the squeezing ratio. Furthermore, we prove that under certain mild conditions, a non-linear resolvent is a starlike mapping of a specified order. As a key tool, we first introduce a refined version of the inverse function theorem for mappings satisfying so-called one-sided estimates. |
| title | Non-linear resolvents of holomorphically accretive mappings |
| topic | Complex Variables |
| url | https://arxiv.org/abs/2406.02758 |