{"paper":{"title":"Radius of convexity of partial sums of odd functions in the close-to-convex family","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CV","authors_text":"Sarita Agrawal, Swadesh Kumar Sahoo","submitted_at":"2016-04-19T10:10:33Z","abstract_excerpt":"We consider the class of all analytic and locally univalent functions $f$ of the form $f(z)=z+\\sum_{n=2}^\\infty a_{2n-1} z^{2n-1}$, $|z|<1$, satisfying the condition $$ {\\rm Re}\\,\\left(1+\\frac{zf^{\\prime\\prime}(z)}{f^\\prime (z)}\\right)>-\\frac{1}{2}. $$ We show that every section $s_{2n-1}(z)=z+\\sum_{k=2}^na_{2k-1}z^{2k-1}$, of $f$, is convex in the disk $|z|<\\sqrt{2}/3$. We also prove that the radius $\\sqrt{2}/3$ is best possible, i.e. the number $\\sqrt{2}/3$ cannot be replaced by a larger one."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1604.05500","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"}