{"paper":{"title":"Generalized Zalcman conjecture for some classes of analytic functions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CV","authors_text":"Shelly Verma, V. Ravichandran","submitted_at":"2016-10-21T12:29:10Z","abstract_excerpt":"For functions $f(z)= z+ a_2 z^2 + a_3 z^3 + \\cdots$ in various subclasses of normalized analytic functions, we consider the problem of estimating the generalized Zalcman coefficient functional $\\phi(f,n,m;\\lambda):=|\\lambda a_n a_m -a_{n+m-1}|$. For all real parameters $\\lambda$ and $ \\beta<1$, we provide the sharp upper bound of $\\phi(f,n,m;\\lambda)$ for functions $f$ satisfying $\\operatorname{Re}f'(z) > \\beta$ and hence settles the open problem of estimating $\\phi(f,n,m;\\lambda)$ recently proposed by Agrawal and Sahoo [S. Agrawal and S. k. Sahoo, On coefficient functionals associated with th"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1610.06760","kind":"arxiv","version":2},"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"}