{"paper":{"title":"Univalence and convexity in one direction of the convolution of harmonic mappings","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CV","authors_text":"Sumit Nagpal, V. Ravichandran","submitted_at":"2013-02-23T12:21:19Z","abstract_excerpt":"Let $\\mathcal{H}$ denote the class of all complex-valued harmonic functions $f$ in the open unit disk normalized by $f(0)=0=f_{z}(0)-1=f_{\\bar{z}}(0)$, and let $\\mathcal{A}$ be the subclass of $\\mathcal{H}$ consisting of normalized analytic functions. For $\\phi \\in \\mathcal{A}$, let $\\mathcal{W}_{H}^{-}(\\phi):=\\{f=h+\\bar{g} \\in \\mathcal{H}:h-g=\\phi\\}$ and $\\mathcal{W}_{H}^{+}(\\phi):=\\{f=h+\\bar{g} \\in \\mathcal{H}:h+g=\\phi\\}$ be subfamilies of $\\mathcal{H}$. In this paper, we shall determine the conditions under which the harmonic convolution $f_1*f_2$ is univalent and convex in one direction if"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1302.5791","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"}