{"paper":{"title":"The radius of univalence of the reciprocal of a product of two analytic functions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CV","authors_text":"\\'A. Baricz, M. Obradovi\\'c, S. Ponnusamy","submitted_at":"2014-12-28T12:33:08Z","abstract_excerpt":"Let ${\\mathcal A}$ denote the family of all functions $f$ analytic in the open unit disk $\\ID$ with the normalization $f(0)=0= f'(0)-1$ and ${\\mathcal S}$ be the class of univalent functions from ${\\mathcal A}$. In this paper, we consider radius of univalence of $F$ defined by $F(z)=z^{3}/(f(z)g(z))$, where $f$ and $g$ belong to some subclasses of ${\\mathcal A}$ (for which $f(z)/z$ and $g(z)/z$ are non-vanishing in $\\ID$) and, in some cases in precise form, belonging to some subclasses of ${\\mathcal S}$. All the results are proved to be sharp. Applications of our investigation through Bessel f"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1412.8158","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"}