{"paper":{"title":"Sufficient Conditions for Starlike Functions Associated with the Lemniscate of Bernoulli","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CV","authors_text":"Nak Eun Cho, S. Sivaprasad Kumar, Virendra Kumar, V. Ravichandran","submitted_at":"2013-03-01T10:33:02Z","abstract_excerpt":"Let -1\\leq B<A\\leq 1. Condition on \\beta, is determined so that 1+\\beta zp'(z)/p^k(z)\\prec(1+Az)/(1+Bz)\\;(-1<k\\leq3) implies p(z)\\prec \\sqrt{1+z}. Similarly, condition on \\beta is determined so that 1+\\beta zp'(z)/p^n(z) or p(z)+\\beta zp'(z)/p^n(z)\\prec\\sqrt{1+z}\\;(n=0, 1, 2) implies p(z)\\prec(1+Az)/(1+Bz) or \\sqrt{1+z}. In addition to that condition on \\beta is derived so that p(z)\\prec(1+Az)/(1+Bz) when p(z)+\\beta zp'(z)/p(z)\\prec\\sqrt{1+z}. Few more problems of the similar flavor are also considered."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1303.0137","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"}