{"paper":{"title":"Starlikeness of the generalized integral transform using duality techniques","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CV","authors_text":"A. Swaminathan, Satwanti Devi","submitted_at":"2014-11-19T13:30:21Z","abstract_excerpt":"For $\\alpha\\geq 0$, $\\delta>0$, $\\beta<1$ and $\\gamma\\geq 0$, the class $\\mathcal{W}_{\\beta}^\\delta(\\alpha,\\gamma)$ consist of analytic and normalized functions $f$ along with the condition \\begin{align*} {\\rm Re\\,} e^{i\\phi}(\\dfrac{}{}(1\\!-\\!\\alpha\\!+\\!2\\gamma)\\!({f}/{z})^\\delta +(\\alpha\\!-\\!3\\gamma\\!+\\!\\gamma[\\dfrac{}{}(1-{1}/{\\delta})({zf'}/{f})+ {1}/{\\delta}(1+{zf''}/{f'})]).\\\\ .\\dfrac{}{}({f}/{z})^\\delta \\!({zf'}/{f})-\\beta)>0, \\end{align*} where $\\phi\\in\\mathbb{R}$ and $|z|<1$, is taken into consideration. The class $\\mathcal{S}^\\ast_s(\\zeta)$ be the subclass of the univalent functions, "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1411.5217","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"}