{"paper":{"title":"Biholomorphic Convex Mappings of Order alpha on the Unit Ball in Hilbert Spaces","license":"http://creativecommons.org/licenses/by/3.0/","headline":"","cross_cats":["math.FA"],"primary_cat":"math.CV","authors_text":"Ming-Sheng Liu, Yu-Can Zhu","submitted_at":"2012-01-21T14:22:32Z","abstract_excerpt":"In this paper, we first introduce the concept of biholomorphic convex mapping of order alpha on the unit ball B in a complex Hilbert space X. Next we provide some sufficient conditions that a locally biholomorphic mapping f is a biholomorphic convex mapping of order alpha and give an Alexander's theorem between the subclass of convex mappings and the subclass of starlike mappings on B in Hilbert space. We also obtain the order of starlikeness of biholomorphic convex mappings of order alpha on B in Hilbert spaces. Finally, we construct some concrete examples of biholomorphic convex mappings of "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1201.4475","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"}