{"paper":{"title":"Criteria for univalence, Integral means and Dirichlet integral for Meromorphic 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":"2017-05-10T08:47:50Z","abstract_excerpt":"Let $\\mathcal{A}(p)$ be the class consisting of functions $f$ that are holomorphic in $\\ID\\setminus \\{p\\}$, $p\\in (0,1)$ possessing a simple pole at the point $z=p$ with nonzero residue and normalized by the condition $f(0)=0=f'(0)-1$. In this article, we first prove a sufficient condition for univalency for functions in $\\mathcal{A}(p)$. Thereafter, we consider the class denoted by $\\Sigma(p)$ that consists of functions $f \\in \\mathcal{A}(p)$ that are univalent in $\\ID$. We obtain the exact value for $\\ds\\max_ {f\\in \\Sigma(p)}\\Delta(r,z/f)$, where the Dirichlet integral $\\Delta(r,z/f)$ is giv"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1705.03663","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"}