{"paper":{"title":"Variability regions of close-to-convex functions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CV","authors_text":"Li-Mei Wang, Takao Kato, Toshiyuki Sugawa","submitted_at":"2011-08-02T02:25:28Z","abstract_excerpt":"M. Biernacki gave concrete forms of the variability regions of $z/f(z)$ and $zf'(z)/f(z)$ of close-to-convex functions $f$ for a fixed $z$ with $|z|<1$ in 1936. The forms are, however, not necessarily convenient to determine the shape of the full variability region of $zf'(z)/f(z)$ over all close-to-convex functions $f$ and all points $z$ with $|z|<1.$ We will propose a couple of other forms of the variability regions and see that the full variability region of $zf'(z)/f(z)$ is indeed the complex plane minus the origin. We also apply them to study the variability regions of $\\log[z/f(z)]$ and "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1108.0461","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"}