{"paper":{"title":"A generalization of starlike functions of order alpha","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CV","authors_text":"Sarita Agrawal, Swadesh K. Sahoo","submitted_at":"2014-04-15T17:10:19Z","abstract_excerpt":"For every $q\\in(0,1)$ and $0\\le \\alpha<1$ we define a class of analytic functions, the so-called $q$-starlike functions of order $\\alpha$, on the open unit disk. We study this class of functions and explore some inclusion properties with the well-known class of starlike functions of order $\\alpha$. The paper is also devoted to the discussion on the Herglotz representation formula for analytic functions $zf'(z)/f(z)$ when $f(z)$ is $q$-starlike of order $\\alpha$. As an application we also discuss the Bieberbach conjecture problem for the $q$-starlike functions of order $\\alpha$. Further applica"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1404.3988","kind":"arxiv","version":2},"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"}