{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2013:UBESZXMSCMD3R7EDZZEEHGR4DF","short_pith_number":"pith:UBESZXMS","schema_version":"1.0","canonical_sha256":"a0492cdd921307b8fc83ce48439a3c1968a5d107e2091d07a702086bdadd0d2f","source":{"kind":"arxiv","id":"1305.0732","version":1},"attestation_state":"computed","paper":{"title":"Order of convexity of Integral Transforms and Duality","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CV","authors_text":"Sarika Verma, Sukhjit Singh, Sushma Gupta","submitted_at":"2013-05-03T14:47:56Z","abstract_excerpt":"Recently, Ali et al defined the class $\\mathcal{W}_{\\beta}(\\alpha, \\gamma)$ consisting of functions $f$ which satisfy $$\\Re e^{i\\phi}\\left((1-\\alpha+2\\gamma)\\frac{f(z)}{z}+(\\alpha-2\\gamma)f'(z)+\\gamma zf''(z)-\\beta\\right)>0,$$ for all $z\\in E=\\left\\{z : |z|<1\\right\\}$ and for $\\alpha, \\gamma\\geq0$ and $\\beta<1$, $\\phi\\in \\mathbb{R}$ (the set of reals). For $f\\in{\\mathcal{W}_{\\beta}(\\alpha, \\gamma)}$, they discussed the convexity of the integral transform $$V_{\\lambda}(f)(z):=\\int_{0}^{1}\\lambda(t)\\frac{f(tz)}{t}dt,$$ where $\\lambda$ is a non-negative real-valued integrable function satisfying "},"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":"1305.0732","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2013-05-03T14:47:56Z","cross_cats_sorted":[],"title_canon_sha256":"d6cf5273828ce9f189298509581b93cff84907c8b5ce107f0e043d3059d69995","abstract_canon_sha256":"7a4debc0b2225059cca2c004cc1e92f159113564f5a95538733787aea9aea593"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:26:32.978154Z","signature_b64":"jbg7naqU5I39scoxq0gze1yfLcnDp9mnlJjq0cnd0iJ5VetDH0vAi18GncP4/KZFWilJY52ZJAdCd6da7W9wBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"a0492cdd921307b8fc83ce48439a3c1968a5d107e2091d07a702086bdadd0d2f","last_reissued_at":"2026-05-18T03:26:32.977678Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:26:32.977678Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Order of convexity of Integral Transforms and Duality","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CV","authors_text":"Sarika Verma, Sukhjit Singh, Sushma Gupta","submitted_at":"2013-05-03T14:47:56Z","abstract_excerpt":"Recently, Ali et al defined the class $\\mathcal{W}_{\\beta}(\\alpha, \\gamma)$ consisting of functions $f$ which satisfy $$\\Re e^{i\\phi}\\left((1-\\alpha+2\\gamma)\\frac{f(z)}{z}+(\\alpha-2\\gamma)f'(z)+\\gamma zf''(z)-\\beta\\right)>0,$$ for all $z\\in E=\\left\\{z : |z|<1\\right\\}$ and for $\\alpha, \\gamma\\geq0$ and $\\beta<1$, $\\phi\\in \\mathbb{R}$ (the set of reals). For $f\\in{\\mathcal{W}_{\\beta}(\\alpha, \\gamma)}$, they discussed the convexity of the integral transform $$V_{\\lambda}(f)(z):=\\int_{0}^{1}\\lambda(t)\\frac{f(tz)}{t}dt,$$ where $\\lambda$ is a non-negative real-valued integrable function satisfying "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1305.0732","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":"1305.0732","created_at":"2026-05-18T03:26:32.977743+00:00"},{"alias_kind":"arxiv_version","alias_value":"1305.0732v1","created_at":"2026-05-18T03:26:32.977743+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1305.0732","created_at":"2026-05-18T03:26:32.977743+00:00"},{"alias_kind":"pith_short_12","alias_value":"UBESZXMSCMD3","created_at":"2026-05-18T12:28:02.375192+00:00"},{"alias_kind":"pith_short_16","alias_value":"UBESZXMSCMD3R7ED","created_at":"2026-05-18T12:28:02.375192+00:00"},{"alias_kind":"pith_short_8","alias_value":"UBESZXMS","created_at":"2026-05-18T12:28:02.375192+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/UBESZXMSCMD3R7EDZZEEHGR4DF","json":"https://pith.science/pith/UBESZXMSCMD3R7EDZZEEHGR4DF.json","graph_json":"https://pith.science/api/pith-number/UBESZXMSCMD3R7EDZZEEHGR4DF/graph.json","events_json":"https://pith.science/api/pith-number/UBESZXMSCMD3R7EDZZEEHGR4DF/events.json","paper":"https://pith.science/paper/UBESZXMS"},"agent_actions":{"view_html":"https://pith.science/pith/UBESZXMSCMD3R7EDZZEEHGR4DF","download_json":"https://pith.science/pith/UBESZXMSCMD3R7EDZZEEHGR4DF.json","view_paper":"https://pith.science/paper/UBESZXMS","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1305.0732&json=true","fetch_graph":"https://pith.science/api/pith-number/UBESZXMSCMD3R7EDZZEEHGR4DF/graph.json","fetch_events":"https://pith.science/api/pith-number/UBESZXMSCMD3R7EDZZEEHGR4DF/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/UBESZXMSCMD3R7EDZZEEHGR4DF/action/timestamp_anchor","attest_storage":"https://pith.science/pith/UBESZXMSCMD3R7EDZZEEHGR4DF/action/storage_attestation","attest_author":"https://pith.science/pith/UBESZXMSCMD3R7EDZZEEHGR4DF/action/author_attestation","sign_citation":"https://pith.science/pith/UBESZXMSCMD3R7EDZZEEHGR4DF/action/citation_signature","submit_replication":"https://pith.science/pith/UBESZXMSCMD3R7EDZZEEHGR4DF/action/replication_record"}},"created_at":"2026-05-18T03:26:32.977743+00:00","updated_at":"2026-05-18T03:26:32.977743+00:00"}