{"paper":{"title":"Value regions of univalent self-maps with two boundary fixed points","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CV","authors_text":"Dmitri Prokhorov, Pavel Gumenyuk","submitted_at":"2017-03-16T21:54:31Z","abstract_excerpt":"In this paper we find the exact value region $\\mathcal V(z_0,T)$ of the point evaluation functional $f\\mapsto f(z_0)$ over the class of all holomorphic injective self-maps $f:\\mathbb D\\to\\mathbb D$ of the unit disk $\\mathbb D$ having a boundary regular fixed point at $\\sigma=-1$ with $f'(-1)=e^{T}$ and the Denjoy - Wolff point at $\\tau=1$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1703.05835","kind":"arxiv","version":2},"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"}