{"paper":{"title":"Geometric studies on the class ${\\mathcal U}(\\lambda)$","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":"2015-03-09T12:24:39Z","abstract_excerpt":"The article deals with the family ${\\mathcal U}(\\lambda)$ of all functions $f$ normalized and analytic in the unit disk such that $\\big |\\big (z/f(z)\\big )^{2}f'(z)-1\\big |<\\lambda $ for some $0<\\lambda \\leq 1$. The family ${\\mathcal U}(\\lambda)$ has been studied extensively in the recent past and functions in this family are known to be univalent in $\\ID$. However, the problem of determining sharp bounds for the second coefficients of functions in this family was solved recently in \\cite{VY2013} by Vasudevarao and Yanagihara but the proof was complicated. In this article, we first present a s"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1503.02451","kind":"arxiv","version":3},"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"}