{"paper":{"title":"Some Results of The Class of Functions with Bounded Radius Rotation","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CV","authors_text":"Arzu Yemi\\c{s}\\c{c}i \\c{S}en, Ya\\c{s}ar Polato\\u{g}lu, Yasemin Kahramaner","submitted_at":"2017-05-03T07:48:33Z","abstract_excerpt":"Let $\\mathcal{A}$ be the family of functions $f(z)=z+a_2z^2+...$ which are analytic in the open unit disc $\\mathbb{D}=\\{z: |z|<1 \\}$, and denote by $\\pe$ of functions $p(z)=z+p_1z+p_2z^2+...$ analytic in $\\de$ such that $p(z)$ is in $\\pe$ if and only if\n  $$p(z)\\prec \\frac{1+z}{1-z} \\Leftrightarrow p(z)=\\frac{1+\\phi(z)}{1-\\phi(z)}, $$ for some Schwarz function $\\phi(z)$ and every $z\\in\\de.$\n  Let $f(z)$ be an element of $\\mathcal{A}$, and satisfies the condition $$z\\frac{f'(z)}{f(z)}=\\left(\\frac{k}{4}+\\frac{1}{2}\\right)p_{1}(z)-\\left(\\frac{k}{4}-\\frac{1}{2}\\right)p_{2}(z)$$ where $p_1(z), p_2("},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1705.01288","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"}