{"paper":{"title":"Sufficient conditions for univalence and study of a class of meromorphic univalent functions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CV","authors_text":"Bappaditya Bhowmik, Firdoshi Parveen","submitted_at":"2017-05-17T05:02:08Z","abstract_excerpt":"In this article we consider the class $\\mathcal{A}(p)$ which consists of functions that are meromorphic in the unit disc $\\ID$ having a simple pole at $z=p\\in (0,1)$ with the normalization $f(0)=0=f'(0)-1 $. First we prove some sufficient conditions for univalence of such functions in $\\ID$. One of these conditions enable us to consider the class $\\mathcal{V}_{p}(\\lambda)$ that consists of functions satisfying certain differential inequality which forces univalence of such functions. Next we establish that $\\mathcal{U}_{p}(\\lambda)\\subsetneq \\mathcal{V}_{p}(\\lambda)$, where $\\mathcal{U}_{p}(\\l"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1705.06009","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"}