{"paper":{"title":"On relations between the classes $\\mathcal S$ and $\\mathcal U$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CV","authors_text":"Karl-Joachim Wirths, Milutin Obradovi\\'c, Saminathan Ponnusamy","submitted_at":"2016-04-26T16:07:42Z","abstract_excerpt":"Let ${\\mathcal A}$ denote the family of all functions $f$ analytic in the unit disk $\\ID$ and satisfying the normalization $f(0)=0= f'(0)-1$. Let $\\mathcal{S}$ denote the subclass of ${\\mathcal A}$ consisting of univalent functions in $\\ID$. We consider the subclass $\\mathcal{U} $ of $\\mathcal{S}$ that is defined by the condition that for its members $f$ the condition $$\\left |\\left (\\frac{z}{f(z)} \\right )^{2}f'(z)-1\\right | < 1 ~\\mbox{ for $z\\in \\ID$} $$ holds. To theses relations belong striking similarities and on the other hand big differences. We show that some results about $\\mathcal{S}"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1604.07733","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"}