{"paper":{"title":"On starlikeness of $p$-valent analytic functions","license":"http://creativecommons.org/publicdomain/zero/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CV","authors_text":"Janusz Sokol, Mamoru Nunokawa$","submitted_at":"2026-05-18T16:05:21Z","abstract_excerpt":"The known Ozaki's condition says that $\\mathfrak{Re}\\left\\{f^{(p)}(z)\\right\\}>0$ for $|z|<1$ implies that $f(z)=z^p+a_{p+1}z^{p+1}+\\cdots$ is at most $p$-valent in $\\mathbb D$. In this paper prove an extension of Ozaki's condition. Also, we shall determine the new sufficient conditions for functions to be in the class of $p$-valent starlike of order $\\alpha$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2605.18590","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/2605.18590/integrity.json","findings":[],"available":true,"detectors_run":[{"name":"claim_evidence","ran_at":"2026-05-20T00:01:59.285882Z","status":"completed","version":"1.0.0","findings_count":0}],"snapshot_sha256":"7c26625afeb594d10cbfdc394280a7cbfa0d4b8b87d0def26ad08cda1b1b52e1"},"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"}