{"paper":{"title":"On the polar derivative of a polynomial","license":"http://creativecommons.org/licenses/publicdomain/","headline":"","cross_cats":[],"primary_cat":"math.CV","authors_text":"N. A. Rather, S. H. Ahangar, Suhail Gulzar","submitted_at":"2014-03-10T15:41:00Z","abstract_excerpt":"Let $P(z)$ be a polynomial of degree $n$ having no zero in $|z|<k$ where $k\\geq 1,$ then for every real or complex number $\\alpha$ with $|\\alpha|\\geq 1$ it is known \\begin{equation*} \\underset{|z|=1}{\\max}|D_\\alpha P(z)|\\leq n\\left(\\dfrac{|\\alpha|+k}{1+k}\\right)\\underset{|z|=1}{\\max}|P(z)|, \\end{equation*} where $D_\\alpha P(z)=nP(z)+(\\alpha-z)P^{\\prime}(z)$ denote the polar derivative of the polynomial $P(z)$ of degree $n$ with respect to a point $\\alpha\\in\\mathbb{C}.$ In this paper, by a simple method, a refinement of above inequality and other related results are obtained."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1403.2270","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"}