{"paper":{"title":"A generalization of Livingston's coefficient inequalities for functions with positive real part","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CV","authors_text":"Iason Efraimidis","submitted_at":"2015-06-23T17:55:39Z","abstract_excerpt":"For functions $p(z) = 1 + \\sum_{n=1}^\\infty p_n z^n$ holomorphic in the unit disk, satisfying $ {\\rm Re}\\, p(z) > 0$, we generalize two inequalities proved by Livingston in 1969 and 1985, and simplify their proofs. One of our results states that $|p_n -w p_k p_{n-k}|\\leq 2\\max\\{1, |1-2w|\\}, w\\in\\mathbb{C}$. Another result involves certain determinants whose entries are the coefficients $p_n$. Both results are sharp. As applications we provide a simple proof of a theorem of J.E. Brown and various inequalities for the coefficients of holomorphic self-maps of the unit disk."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1506.07111","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"}