{"paper":{"title":"On the Taylor coefficients of a subclass 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":"2017-12-08T06:35:32Z","abstract_excerpt":"Let $\\mathcal{V}_p(\\lambda)$ be the collection of all functions $f$ defined in the unit disc $\\ID$ having a simple pole at $z=p$ where $0<p<1$ and analytic in $\\ID\\setminus\\{p\\}$ with $f(0)=0=f'(0)-1$ and satisfying the differential inequality $|(z/f(z))^2 f'(z)-1|< \\lambda $ for $z\\in \\ID$, $0<\\lambda\\leq 1$. Each $f\\in\\mathcal{V}_p(\\lambda)$ has the following Taylor expansion:\n  $$\n  f(z)=z+\\sum_{n=2}^{\\infty}a_n(f) z^n, \\quad |z|<p.\n  $$\n  In \\cite{BF-3}, we conjectured that\n  $$\n  |a_n(f)|\\leq \\frac{1-(\\lambda p^2)^n}{p^{n-1}(1-\\lambda p^2)}\\quad \\mbox{for}\\quad n\\geq3. $$ In the present a"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1712.02958","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"}