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In this paper, we study bounds for the logarithmic coefficients for certain subfamilies of univalent functions. Also, we consider the families $\\F(c)$ and $\\G(\\delta)$ of functions $f\\in {\\es}$ defined by $$ {\\rm Re} \\left ( 1+\\frac{zf''(z)}{f'(z)}\\right )>1-\\frac{c}{2}\\, \\mbox{ and } \\, {\\rm Re} \\left ( 1+\\frac{zf''(z)}{f'(z)}\\right )<1+\\frac{\\delta}{2},\\quad z\\in \\D $$ for some $c\\in("},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1811.01203","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2018-11-03T12:59:51Z","cross_cats_sorted":[],"title_canon_sha256":"d36ee19a0571db2de0e2216b4c8c0b48c50bdb81b02ad40c1c9dd368b4a2a4b0","abstract_canon_sha256":"b64f3515d629012833301c65a639f75cb9f56389689a4eca51132227b6e4e8c9"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:01:35.031727Z","signature_b64":"ldPw8lp0Bae7iFQgkzAscv1E512trTCyRbCVoGOR4MdvuGr8ix8BCGj+oE1vfxitolmFdmvkrYjdFR4FAkBpAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"2d69031102b861d69f2648993c18a77b1b8ddd2160e07484a55db3ac6a316e2c","last_reissued_at":"2026-05-18T00:01:35.031011Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:01:35.031011Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Logarithmic coefficients problems in families related to starlike and convex functions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CV","authors_text":"K.-J. Wirths, N. L. Sharma, S. Ponnusamy","submitted_at":"2018-11-03T12:59:51Z","abstract_excerpt":"Let $\\es$ be the family of analytic and univalent functions $f$ in the unit disk $\\D$ with the normalization $f(0)=f'(0)-1=0$, and let $\\gamma_n(f)=\\gamma_n$ denote the logarithmic coefficients of $f\\in {\\es}$. In this paper, we study bounds for the logarithmic coefficients for certain subfamilies of univalent functions. Also, we consider the families $\\F(c)$ and $\\G(\\delta)$ of functions $f\\in {\\es}$ defined by $$ {\\rm Re} \\left ( 1+\\frac{zf''(z)}{f'(z)}\\right )>1-\\frac{c}{2}\\, \\mbox{ and } \\, {\\rm Re} \\left ( 1+\\frac{zf''(z)}{f'(z)}\\right )<1+\\frac{\\delta}{2},\\quad z\\in \\D $$ for some $c\\in("},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1811.01203","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"},"aliases":[{"alias_kind":"arxiv","alias_value":"1811.01203","created_at":"2026-05-18T00:01:35.031116+00:00"},{"alias_kind":"arxiv_version","alias_value":"1811.01203v1","created_at":"2026-05-18T00:01:35.031116+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1811.01203","created_at":"2026-05-18T00:01:35.031116+00:00"},{"alias_kind":"pith_short_12","alias_value":"FVUQGEICXBQ5","created_at":"2026-05-18T12:32:25.280505+00:00"},{"alias_kind":"pith_short_16","alias_value":"FVUQGEICXBQ5NHZG","created_at":"2026-05-18T12:32:25.280505+00:00"},{"alias_kind":"pith_short_8","alias_value":"FVUQGEIC","created_at":"2026-05-18T12:32:25.280505+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/FVUQGEICXBQ5NHZGJCMTYGFHPM","json":"https://pith.science/pith/FVUQGEICXBQ5NHZGJCMTYGFHPM.json","graph_json":"https://pith.science/api/pith-number/FVUQGEICXBQ5NHZGJCMTYGFHPM/graph.json","events_json":"https://pith.science/api/pith-number/FVUQGEICXBQ5NHZGJCMTYGFHPM/events.json","paper":"https://pith.science/paper/FVUQGEIC"},"agent_actions":{"view_html":"https://pith.science/pith/FVUQGEICXBQ5NHZGJCMTYGFHPM","download_json":"https://pith.science/pith/FVUQGEICXBQ5NHZGJCMTYGFHPM.json","view_paper":"https://pith.science/paper/FVUQGEIC","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1811.01203&json=true","fetch_graph":"https://pith.science/api/pith-number/FVUQGEICXBQ5NHZGJCMTYGFHPM/graph.json","fetch_events":"https://pith.science/api/pith-number/FVUQGEICXBQ5NHZGJCMTYGFHPM/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/FVUQGEICXBQ5NHZGJCMTYGFHPM/action/timestamp_anchor","attest_storage":"https://pith.science/pith/FVUQGEICXBQ5NHZGJCMTYGFHPM/action/storage_attestation","attest_author":"https://pith.science/pith/FVUQGEICXBQ5NHZGJCMTYGFHPM/action/author_attestation","sign_citation":"https://pith.science/pith/FVUQGEICXBQ5NHZGJCMTYGFHPM/action/citation_signature","submit_replication":"https://pith.science/pith/FVUQGEICXBQ5NHZGJCMTYGFHPM/action/replication_record"}},"created_at":"2026-05-18T00:01:35.031116+00:00","updated_at":"2026-05-18T00:01:35.031116+00:00"}