{"paper":{"title":"Coefficient Inequalities for Concave and Meromorphically Starlike Univalent Functions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CV","authors_text":"Bappaditya Bhowmik, Saminathan Ponnusamy","submitted_at":"2010-08-28T12:46:52Z","abstract_excerpt":"Let $\\ID$ denote the open unit disk and $f:\\,\\ID\\TO\\BAR\\IC$ be meromorphic and univalent in $\\ID$ with the simple pole at $p\\in (0,1)$ and satisfying the standard normalization $f(0)=f'(0)-1=0$. Also, let $f$ have the expansion $$f(z)=\\sum_{n=-1}^{\\infty}a_n(z-p)^n,\\quad |z-p|<1-p, $$ such that $f$ maps $\\ID$ onto a domain whose complement with respect to $\\BAR{\\IC}$ is a convex set (starlike set with respect to a point $w_0\\in \\IC, w_0\\neq 0$ resp.). We call these functions as concave (meromorphically starlike resp.) univalent functions and denote this class by $Co(p)$ $(\\Sigma^s(p, w_0)$ res"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1008.4860","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"}