{"paper":{"title":"Order of Starlikeness and Convexity of certain integral transforms 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":"2014-06-25T06:31:29Z","abstract_excerpt":"For $\\alpha\\geq 0$, $\\beta<1$ and $\\gamma\\geq 0$, the class $\\mathcal{W}_{\\beta}(\\alpha,\\gamma)$ satisfies the condition \\begin{align*} {\\rm Re\\,} \\left( e^{i\\phi}\\left((1-\\alpha+2\\gamma)f/z+(\\alpha-2\\gamma)f'+ \\gamma zf''-\\beta\\right)\\frac{}{}\\right)>0, \\quad \\phi\\in {\\mathbb{R}},{\\,}z\\in {\\mathbb{D}}; \\end{align*} is taken into consideration. The Pascu class of $\\xi$-convex functions of order $\\sigma$ $(M(\\sigma,{\\,}\\xi))$, having analytic characterization \\begin{align*} {\\rm Re\\,}\\frac{\\xi z(zf'(z))'+(1-\\xi)zf'(z)}{\\xi zf'(z)+(1-\\xi)f(z)}>\\sigma,\\quad 0\\leq \\sigma< 1,\\quad z\\in {\\mathbb{D}}"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1406.6471","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"}