{"paper":{"title":"Complementary Inequalities to Improved AM-GM Inequality","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"H.R. Moradi, M.E. Omidvar","submitted_at":"2017-06-26T11:56:18Z","abstract_excerpt":"Following an idea of Lin, we prove that if $A$ and $B$ be two positive operators such that $0<mI\\le A\\le m'I\\le M'I\\le B\\le MI$, then \\begin{equation*} {{\\Phi }^{2}}\\left( \\frac{A+B}{2} \\right)\\le \\frac{{{K}^{2}}\\left( h \\right)}{{{\\left( 1+\\frac{{{\\left( \\log \\frac{M'}{m'} \\right)}^{2}}}{8} \\right)}^{2}}}{{\\Phi }^{2}}\\left( A\\#B \\right), \\end{equation*} and \\begin{equation*} {{\\Phi }^{2}}\\left( \\frac{A+B}{2} \\right)\\le \\frac{{{K}^{2}}\\left( h \\right)}{{{\\left( 1+\\frac{{{\\left( \\log \\frac{M'}{m'} \\right)}^{2}}}{8} \\right)}^{2}}}{{\\left( \\Phi \\left( A \\right)\\#\\Phi \\left( B \\right) \\right)}^{2}"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1706.08331","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"}