{"paper":{"title":"Invariance of the Initial Coefficient Differences of Ma-Minda Convex Functions","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.CV","authors_text":"Mohsan Raza, Rashid Ali, Umar Raza","submitted_at":"2026-06-11T09:38:20Z","abstract_excerpt":"Let $\\Phi $ be a univalent function in $\\mathbb{D}=\\{z\\in \\mathbb{C}:|z|<1\\}$% , $\\Phi (\\mathbb{D})$ is symmetric with respect to the real axis, starlike with respect to $\\Phi (0)=1$, and $\\Phi ^{\\prime }(0)>0$. Let $\\mathcal{C}% (\\Phi )$ denote the class of Ma-Minda convex functions. In this article, we present the bounds on $||a_{3}|-|a_{2}||$ for Taylor's coefficients of the function $f$ in the class $\\mathcal{C}(\\Phi )$. We also establish the same bounds for the inverse coefficients. All the bounds we study here are sharp. We also present the conditions such that the bounds on $|a_{3}|-|a_"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.13112","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/2606.13112/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"}