{"paper":{"title":"On a problem of Bharanedhar and Ponnusamy involving planar harmonic mappings","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CV","authors_text":"Antti Rasila, Yong Sun, Zhi-Gang Wang, Zhi-Hong Liu","submitted_at":"2017-03-28T09:47:51Z","abstract_excerpt":"In this paper, we give a negative answer to a problem presented by Bharanedhar and Ponnusamy (Rocky Mountain J. Math. 44: 753--777, 2014) concerning univalency of a class of harmonic mappings. More precisely, we show that for all values of the involved parameter, this class contains a non-univalent function. Moreover, several results on a new subclass of close-to-convex harmonic mappings, which is motivated by work of Ponnusamy and Sairam Kaliraj (Mediterr. J. Math. 12: 647--665, 2015), are obtained."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1703.09478","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"}