{"paper":{"title":"Radius of convexity of certain classes of functions defined by convolution","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CV","authors_text":"Bappaditya Bhowmik, Souvik Biswas","submitted_at":"2026-06-18T19:02:10Z","abstract_excerpt":"Let $\\mathcal{S}$ be the class of analytic univalent functions defined in the open unit disc $\\mathbb{D}$ of the complex plane with the normalizations $f(0)=0$ and $f'(0)=1$. For $A\\in (1,2]$, let $Co(A)$ denote the class of concave univalent functions defined in $\\mathbb{D}$ with the opening angle $\\pi A$ at infinity. In this article, by applying certain convolution techniques, we investigate the radius of convexity for the class $Co(A)\\ast\\mathcal{S}t(1/2)$, where $\\mathcal{S}t(1/2)\\subsetneq \\mathcal{S}$ denotes the class of starlike functions of order $1/2$. Furthermore, we establish that "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.20872","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2606.20872/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"}