{"paper":{"title":"Three Value Ranges for Symmetric Self-mappings","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CV","authors_text":"Julia Koch, Sebastian Schlei{\\ss}inger","submitted_at":"2016-02-16T15:42:06Z","abstract_excerpt":"Let $\\mathbb D$ be the unit disc and $z_0\\in\\mathbb D.$ We determine the value range $\\{f(z_0)\\,|\\, f\\in \\mathcal{R}^\\geq\\}$, where $\\mathcal{R}^\\geq$ is the set of holomorphic functions $f:\\mathbb D\\to\\mathbb D$ with $f(0)=0$ and $f'(0)\\geq0$ that have only real coefficients in their power series expansion around $0$, and the smaller set $\\{f(z_0)\\,|\\, f\\in \\mathcal{R}^\\geq, \\text{$f$ is typically real}\\}.$ Furthermore, we describe a third value range $\\{ f(z_0) \\,|\\, f \\in \\mathcal{I}\\}$, where $\\mathcal{I}$ consists of all univalent self-mappings of the upper half-plane $\\mathbb{H}$ with hy"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1602.05058","kind":"arxiv","version":3},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}