{"paper":{"title":"Convolution properties of univalent harmonic mappings convex in one direction","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CV","authors_text":"Raj Kumar, Sukhjit Singh, Sushma Gupta","submitted_at":"2014-01-01T07:00:48Z","abstract_excerpt":"Let $\\ast$ and $\\widetilde {\\ast}$ denote the convolution of two analytic maps and that of an analytic map and a harmonic map respectively. Pokhrel [1] proved that if $f = h+\\overline{g}$ is a harmonic map convex in the direction of $e^{i\\gamma}$ and $\\phi$ is an analytic map in the class DCP, then $f\\widetilde{\\ast} \\phi= h\\widetilde{\\ast}\\phi + \\overline{g\\widetilde{\\ast}\\phi}$ is also convex in the direction of $e^{i\\gamma}$, provided $f\\widetilde{\\ast}\\phi$ is locally univalent and sense-preserving. In the present paper we obtain a general condition under which $f\\widetilde{\\ast} \\phi$ is "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1401.0259","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"}