{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2019:NF3BYADL3IDXUEMBKLRYY6JYDV","short_pith_number":"pith:NF3BYADL","schema_version":"1.0","canonical_sha256":"69761c006bda077a118152e38c79381d577fff9e81d27b923ae8cc8801144106","source":{"kind":"arxiv","id":"1906.03010","version":1},"attestation_state":"computed","paper":{"title":"Stability of Euler-Lagrange type cubic functional equations in quasi-Banach spaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Anurak Thanyacharoen, Nguyen Van Dung, Wutiphol Sintunavarat","submitted_at":"2019-06-07T11:08:43Z","abstract_excerpt":"In this paper, we study the generalized Hyers-Ulam stability of Euler-Lagrange type cubic functional equation of the form \\begin{align*} 2mf(x + my) + 2f(mx - y) = (m^3 + m)[f(x+ y) + f(x - y)] + 2(m^4 - 1)f(y) \\end{align*} for all $x,y \\in X$, where $m$ is a fixed scalar such that $m \\neq 0,1$, and $f$ is a map from a quasi-normed space $X$ to a quasi-Banach space $Y$ over the same field with $X$ by applying the alternative fixed point theorem."},"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":"1906.03010","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2019-06-07T11:08:43Z","cross_cats_sorted":[],"title_canon_sha256":"844ca3da398dbce261704d7365b46f32999016431feae5ba3e080f9f5ff56648","abstract_canon_sha256":"481e0e985795c7303b5d5f86f0a20d62730d0e0638848e087c2fa0715ebcc08e"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:43:55.374806Z","signature_b64":"+y/89UkVkdKSx/0wUx4BREDXwVMT43dZZndQtkcR37BVXC1L1FCbIb66Hi1EedOGLIDtLS73RY1yl/4YYGL5Cg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"69761c006bda077a118152e38c79381d577fff9e81d27b923ae8cc8801144106","last_reissued_at":"2026-05-17T23:43:55.374112Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:43:55.374112Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Stability of Euler-Lagrange type cubic functional equations in quasi-Banach spaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Anurak Thanyacharoen, Nguyen Van Dung, Wutiphol Sintunavarat","submitted_at":"2019-06-07T11:08:43Z","abstract_excerpt":"In this paper, we study the generalized Hyers-Ulam stability of Euler-Lagrange type cubic functional equation of the form \\begin{align*} 2mf(x + my) + 2f(mx - y) = (m^3 + m)[f(x+ y) + f(x - y)] + 2(m^4 - 1)f(y) \\end{align*} for all $x,y \\in X$, where $m$ is a fixed scalar such that $m \\neq 0,1$, and $f$ is a map from a quasi-normed space $X$ to a quasi-Banach space $Y$ over the same field with $X$ by applying the alternative fixed point theorem."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1906.03010","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":"1906.03010","created_at":"2026-05-17T23:43:55.374237+00:00"},{"alias_kind":"arxiv_version","alias_value":"1906.03010v1","created_at":"2026-05-17T23:43:55.374237+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1906.03010","created_at":"2026-05-17T23:43:55.374237+00:00"},{"alias_kind":"pith_short_12","alias_value":"NF3BYADL3IDX","created_at":"2026-05-18T12:33:24.271573+00:00"},{"alias_kind":"pith_short_16","alias_value":"NF3BYADL3IDXUEMB","created_at":"2026-05-18T12:33:24.271573+00:00"},{"alias_kind":"pith_short_8","alias_value":"NF3BYADL","created_at":"2026-05-18T12:33:24.271573+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/NF3BYADL3IDXUEMBKLRYY6JYDV","json":"https://pith.science/pith/NF3BYADL3IDXUEMBKLRYY6JYDV.json","graph_json":"https://pith.science/api/pith-number/NF3BYADL3IDXUEMBKLRYY6JYDV/graph.json","events_json":"https://pith.science/api/pith-number/NF3BYADL3IDXUEMBKLRYY6JYDV/events.json","paper":"https://pith.science/paper/NF3BYADL"},"agent_actions":{"view_html":"https://pith.science/pith/NF3BYADL3IDXUEMBKLRYY6JYDV","download_json":"https://pith.science/pith/NF3BYADL3IDXUEMBKLRYY6JYDV.json","view_paper":"https://pith.science/paper/NF3BYADL","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1906.03010&json=true","fetch_graph":"https://pith.science/api/pith-number/NF3BYADL3IDXUEMBKLRYY6JYDV/graph.json","fetch_events":"https://pith.science/api/pith-number/NF3BYADL3IDXUEMBKLRYY6JYDV/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/NF3BYADL3IDXUEMBKLRYY6JYDV/action/timestamp_anchor","attest_storage":"https://pith.science/pith/NF3BYADL3IDXUEMBKLRYY6JYDV/action/storage_attestation","attest_author":"https://pith.science/pith/NF3BYADL3IDXUEMBKLRYY6JYDV/action/author_attestation","sign_citation":"https://pith.science/pith/NF3BYADL3IDXUEMBKLRYY6JYDV/action/citation_signature","submit_replication":"https://pith.science/pith/NF3BYADL3IDXUEMBKLRYY6JYDV/action/replication_record"}},"created_at":"2026-05-17T23:43:55.374237+00:00","updated_at":"2026-05-17T23:43:55.374237+00:00"}