{"paper":{"title":"Convolution of a harmonic mapping with $n$-starlike mappings and its partial sums","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CV","authors_text":"Subzar Beig, V. Ravichandran","submitted_at":"2017-03-10T09:34:27Z","abstract_excerpt":"We investigate the univalency and the directional convexity of the convolution $\\phi\\tilde{*}f=\\phi*h+\\overline{\\phi*g}$ of the harmonic mapping $f=h+\\bar{g}$ with a mapping $\\phi$ whose convolution with the mapping $z+\\sum_{k=2}^{\\infty}k^nz^k$ is starlike (and such a mapping $\\phi$ is called $n$-starlike). In addition, we investigate the directional convexity of (i) the convolution of an analytic convex mapping with the slanted half-plane mapping, and (ii) the partial sums of the convolution of a $6$-starlike mapping with the harmonic Koebe mapping and the harmonic half-plane mapping."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1703.03595","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"}