{"paper":{"title":"Univalency of convolutions of univalent harmonic right half-plane mappings","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CV","authors_text":"Saminathan Ponnusamy, Zhihong Liu","submitted_at":"2016-09-17T04:31:04Z","abstract_excerpt":"We consider the convolution of half-plane harmonic mappings with respective dilatations $(z+a)/(1+az)$ and $e^{i\\theta}z^{n}$, where $-1<a<1$ and $\\theta\\in\\mathbb{R},n\\in\\mathbb{N}$. We prove that such convolutions are locally univalent for $n=1$, which solves an open problem of Dorff et. al (see \\cite[Problem~3.26]{Bshouty2010}). Moreover, we provide some numerical computations to illustrate that such convolutions are not univalent for $n\\geq 2$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1609.05282","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"}