{"paper":{"title":"On an inequality concerning the polar derivative of a polynomial with restricted zeros","license":"http://creativecommons.org/licenses/publicdomain/","headline":"","cross_cats":[],"primary_cat":"math.CV","authors_text":"N. A. Rather, Suhail Gulzar","submitted_at":"2014-04-26T04:08:06Z","abstract_excerpt":"Let $D_\\alpha P(z)=nP(z)+(\\alpha-z)P^{\\prime}(z)$ denote the polar derivative of a polynomial $P(z)$ of degree $n$ with respect to a point $\\alpha\\in\\mathbb{C}.$ In this paper, we present a correct proof, independent of Laguerre's theorem, of an inequality concerning the polar derivative of a polynomial with restricted zeros recently formulated by K. K. Dewan, Naresh Singh, Abdullah Mir, [Extensions of some polynomial inequalities to the polar derivative, \\emph{J. Math. Anal. Appl.,} \\textbf{352} (2009) 807-815]."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1404.6600","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"}