{"paper":{"title":"Radius of Close-to-convexity of Harmonic Functions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CV","authors_text":"David Kalaj, Matti Vuorinen, Saminathan Ponnusamy","submitted_at":"2011-07-04T12:38:02Z","abstract_excerpt":"Let ${\\mathcal H}$ denote the class of all normalized complex-valued harmonic functions $f=h+\\bar{g}$ in the unit disk ${\\mathbb D}$, and let $K=H+\\bar{G}$ denote the harmonic Koebe function. Let $a_n,b_n, A_n, B_n$ denote the Maclaurin coefficients of $h,g,H,G$, and $${\\mathcal F}=\\{f=h+\\bar{g}\\in {\\mathcal H}:\\,|a_n|\\leq A_n and |b_n|\\leq B_n for n\\geq 1}. $$ We show that the radius of univalence of the family ${\\mathcal F}$ is $0.112903...$. We also show that this number is also the radius of the starlikeness of ${\\mathcal F}$. Analogous results are proved for a subclass of the class of har"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1107.0610","kind":"arxiv","version":1},"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"}