Non-linear resolvents of holomorphically accretive mappings
Complex Variables
2024-06-06 v1
Abstract
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.
Keywords
Cite
@article{arxiv.2406.02758,
title = {Non-linear resolvents of holomorphically accretive mappings},
author = {Mark Elin},
journal= {arXiv preprint arXiv:2406.02758},
year = {2024}
}