{"paper":{"title":"On Booth lemniscate of starlike functions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CV","authors_text":"A. Ebadian, J. Sok\\'o{\\l}, R. Kargar","submitted_at":"2017-01-26T17:20:17Z","abstract_excerpt":"Assume that $\\Delta$ is the open unit disk in the complex plane and $\\mathcal{A}$ is the class of normalized analytic functions in $\\Delta$. In this paper we introduce and study the class \\begin{equation*}\n  \\mathcal{BS}(\\alpha):=\\left\\{f\\in \\mathcal{A}: \\left(\\frac{zf'(z)}{f(z)}-1\\right)\\prec \\frac{z}{1-\\alpha z^2}, \\, z\\in\\Delta\\right\\}, \\end{equation*} where $0\\leq\\alpha\\leq1$ and $\\prec$ is the subordination relation. Some properties of this class like differential subordination, coefficients estimates and Fekete-Szeg\\\"{o} inequality associated with the $k$-th root transform are considered"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1701.07779","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"}