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Swaminathan, Satwanti Devi","submitted_at":"2013-04-02T17:07:27Z","abstract_excerpt":"Let $W_{\\beta}(\\alpha,\\gamma)$, $\\beta<1$, denote the class of all normalized analytic functions $f$ in the unit disc ${\\mathbb{D}}=\\{z\\in {\\mathbb{C}}: |z|<1\\}$ such that \\begin{align*} {\\rm Re\\,} \\left(e^{i\\phi}\\left((1-\\alpha+2\\gamma)\\frac{f}{z}+(\\alpha-2\\gamma)f'+\\gamma zf\"-\\beta\\right)\\frac{}{}\\right)>0, \\quad z\\in {\\mathbb{D}}, \\end{align*} for some $\\phi\\in {\\mathbb{R}}$ with $\\alpha\\geq 0$, $\\gamma\\geq 0$ and $\\beta< 1$. Let $M(\\xi)$, $0\\leq \\xi\\leq 1$, denote the Pascu class of $\\xi$-convex functions given by the analytic condition \\begin{align*} {\\rm Re\\,}\\frac{\\xi z(zf'(z))'+(1-\\xi)"},"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":"1304.0696","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2013-04-02T17:07:27Z","cross_cats_sorted":[],"title_canon_sha256":"866219a097d2d404599ac4b697b7dc74f83d8a3f311e642035c4649145c795d7","abstract_canon_sha256":"59a8eff03016c6ba34f2131389f462e661055b42367f76255a2f24993cb3e696"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:33:07.894408Z","signature_b64":"Lk4VN1tj/7glFUSMcFx8mQ5j8sGzPQpqY4k0YUKp1Z38BlfgiJ58Ax88QOVkE1r68cWKg4Hj27miVIuxXgsSAQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"6509df3295daafcd5b97043ee0b51791d37535b1cc25f6173aefaab6960eb76c","last_reissued_at":"2026-05-18T02:33:07.893815Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:33:07.893815Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Integral transforms of functions to be in the Pascu class using duality techniques","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CV","authors_text":"A. Swaminathan, Satwanti Devi","submitted_at":"2013-04-02T17:07:27Z","abstract_excerpt":"Let $W_{\\beta}(\\alpha,\\gamma)$, $\\beta<1$, denote the class of all normalized analytic functions $f$ in the unit disc ${\\mathbb{D}}=\\{z\\in {\\mathbb{C}}: |z|<1\\}$ such that \\begin{align*} {\\rm Re\\,} \\left(e^{i\\phi}\\left((1-\\alpha+2\\gamma)\\frac{f}{z}+(\\alpha-2\\gamma)f'+\\gamma zf\"-\\beta\\right)\\frac{}{}\\right)>0, \\quad z\\in {\\mathbb{D}}, \\end{align*} for some $\\phi\\in {\\mathbb{R}}$ with $\\alpha\\geq 0$, $\\gamma\\geq 0$ and $\\beta< 1$. Let $M(\\xi)$, $0\\leq \\xi\\leq 1$, denote the Pascu class of $\\xi$-convex functions given by the analytic condition \\begin{align*} {\\rm Re\\,}\\frac{\\xi z(zf'(z))'+(1-\\xi)"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1304.0696","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":"1304.0696","created_at":"2026-05-18T02:33:07.893900+00:00"},{"alias_kind":"arxiv_version","alias_value":"1304.0696v1","created_at":"2026-05-18T02:33:07.893900+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1304.0696","created_at":"2026-05-18T02:33:07.893900+00:00"},{"alias_kind":"pith_short_12","alias_value":"MUE56MUV3KX4","created_at":"2026-05-18T12:27:52.871228+00:00"},{"alias_kind":"pith_short_16","alias_value":"MUE56MUV3KX42W4X","created_at":"2026-05-18T12:27:52.871228+00:00"},{"alias_kind":"pith_short_8","alias_value":"MUE56MUV","created_at":"2026-05-18T12:27:52.871228+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/MUE56MUV3KX42W4XAQ7OBNIXSH","json":"https://pith.science/pith/MUE56MUV3KX42W4XAQ7OBNIXSH.json","graph_json":"https://pith.science/api/pith-number/MUE56MUV3KX42W4XAQ7OBNIXSH/graph.json","events_json":"https://pith.science/api/pith-number/MUE56MUV3KX42W4XAQ7OBNIXSH/events.json","paper":"https://pith.science/paper/MUE56MUV"},"agent_actions":{"view_html":"https://pith.science/pith/MUE56MUV3KX42W4XAQ7OBNIXSH","download_json":"https://pith.science/pith/MUE56MUV3KX42W4XAQ7OBNIXSH.json","view_paper":"https://pith.science/paper/MUE56MUV","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1304.0696&json=true","fetch_graph":"https://pith.science/api/pith-number/MUE56MUV3KX42W4XAQ7OBNIXSH/graph.json","fetch_events":"https://pith.science/api/pith-number/MUE56MUV3KX42W4XAQ7OBNIXSH/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/MUE56MUV3KX42W4XAQ7OBNIXSH/action/timestamp_anchor","attest_storage":"https://pith.science/pith/MUE56MUV3KX42W4XAQ7OBNIXSH/action/storage_attestation","attest_author":"https://pith.science/pith/MUE56MUV3KX42W4XAQ7OBNIXSH/action/author_attestation","sign_citation":"https://pith.science/pith/MUE56MUV3KX42W4XAQ7OBNIXSH/action/citation_signature","submit_replication":"https://pith.science/pith/MUE56MUV3KX42W4XAQ7OBNIXSH/action/replication_record"}},"created_at":"2026-05-18T02:33:07.893900+00:00","updated_at":"2026-05-18T02:33:07.893900+00:00"}