{"paper":{"title":"On an operator preserving inequalities between polynomials","license":"http://creativecommons.org/licenses/by/3.0/","headline":"","cross_cats":[],"primary_cat":"math.CV","authors_text":"N. A. Rather, Suhail Gulzar","submitted_at":"2013-03-30T05:01:38Z","abstract_excerpt":"Let $\\mathscr{P}_n $ denote the space of all complex polynomials $P(z)=\\sum_{j=0}^{n}a_{j}{z}^{j}$ of degree $n$ and $\\mathcal{B}_n$ a family of operators that maps $\\mathscr{P}_n$ into itself. In this paper, we consider a problem of investigating the dependence of $$|B[P\\circ\\sigma](z)-\\alpha B[P\\circ\\rho](z)+\\beta\\{(\\frac{R+k}{k+r})^{n}-|\\alpha|\\}B[P\\circ\\rho](z)| $$ on the maximum and minimum modulus of $|P(z)|$ on $|z|=k$ for arbitrary real or complex numbers $\\alpha,\\beta\\in\\mathbb{C}$ with $|\\alpha|\\leq 1,|\\beta|\\leq 1,R>r\\geq k,$ $\\sigma(z)=Rz,$ $\\rho(z)=rz$ and establish certain sharp "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1304.0067","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"}