{"paper":{"title":"On Some Subclass of Harmonic Close-to-convex Mappings","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CV","authors_text":"A. Vasudevarao, Nirupam Ghosh","submitted_at":"2016-06-27T06:22:33Z","abstract_excerpt":"Let $\\mathcal{H}$ denote the class of harmonic functions $f$ in $\\mathbb{D}:= \\{z\\in \\mathbb{C}:|z| < 1\\}$ normalized by $f(0) = 0 = f_z(0) -1$. For $\\alpha \\geq 0$, we consider the following class $$\\mathcal{W}^0_{\\mathcal{H}}(\\alpha):= \\{f = h + \\overline{g}\\in\\mathcal{H}: {\\rm Re\\,}(h'(z) + \\alpha z h''(z)) >|g'(z) + \\alpha z g''(z)|, \\quad z\\in \\mathbb{D}\\}. $$ In this paper, we first prove the coefficient conjecture of Clunie and Sheil-Small for functions in the class $\\mathcal{W}^0_{\\mathcal{H}}(\\alpha)$. We also prove growth theorem, convolution, convex combination properties for functi"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1606.08134","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"}