{"paper":{"title":"Convexity of the Generalized Integral Transform and 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":"2014-11-21T14:57:41Z","abstract_excerpt":"Let $\\mathcal{W}_{\\beta}^\\delta(\\alpha,\\gamma)$ be the class of normalized analytic functions $f$ defined in the domain $|z|<1$ satisfying \\begin{align*} {\\rm Re\\,} e^{i\\phi}\\left(\\dfrac{}{}(1\\!-\\!\\alpha\\!+\\!2\\gamma)\\!\\left({f}/{z}\\right)^\\delta +\\left(\\alpha\\!-\\!3\\gamma+\\gamma\\left[\\dfrac{}{}\\left(1-{1}/{\\delta}\\right)\\left({zf'}/{f}\\right)+ {1}/{\\delta}\\left(1+{zf''}/{f'}\\right)\\right]\\right)\\right.\\\\ \\left.\\dfrac{}{}\\left({f}/{z}\\right)^\\delta \\!\\left({zf'}/{f}\\right)-\\beta\\right)>0, \\end{align*} with the conditions $\\alpha\\geq 0$, $\\beta<1$, $\\gamma\\geq 0$, $\\delta>0$ and $\\phi\\in\\mathbb{R"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1411.5898","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"}