{"paper":{"title":"Integral transforms of functions to be in the Pascu class 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":"2013-04-02T17:07:27Z","abstract_excerpt":"Let $W_{\\beta}(\\alpha,\\gamma)$, $\\beta<1$, denote the class of all normalized analytic functions $f$ in the unit disc ${\\mathbb{D}}=\\{z\\in {\\mathbb{C}}: |z|<1\\}$ such that \\begin{align*} {\\rm Re\\,} \\left(e^{i\\phi}\\left((1-\\alpha+2\\gamma)\\frac{f}{z}+(\\alpha-2\\gamma)f'+\\gamma zf\"-\\beta\\right)\\frac{}{}\\right)>0, \\quad z\\in {\\mathbb{D}}, \\end{align*} for some $\\phi\\in {\\mathbb{R}}$ with $\\alpha\\geq 0$, $\\gamma\\geq 0$ and $\\beta< 1$. Let $M(\\xi)$, $0\\leq \\xi\\leq 1$, denote the Pascu class of $\\xi$-convex functions given by the analytic condition \\begin{align*} {\\rm Re\\,}\\frac{\\xi z(zf'(z))'+(1-\\xi)"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1304.0696","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"}