{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2013:3JFCUOIBZTAT4OWWQ3T3HO64LT","short_pith_number":"pith:3JFCUOIB","schema_version":"1.0","canonical_sha256":"da4a2a3901ccc13e3ad686e7b3bbdc5ce62df6a5a44ceb01f9bd65cd88fe6f23","source":{"kind":"arxiv","id":"1307.0653","version":1},"attestation_state":"computed","paper":{"title":"General and alien solutions of a functional equation and of a functional inequality","license":"http://creativecommons.org/licenses/by/3.0/","headline":"","cross_cats":[],"primary_cat":"math.CA","authors_text":"Eszter Gselmann, W{\\l}odzimierz Fechner","submitted_at":"2013-07-02T10:00:12Z","abstract_excerpt":"The purpose of the present paper is to solve (under some assumption on the domain) the equation $$ g(x+y)-g(x)-g(y)=xf(y)+yf(x). $$ After determining the general solutions, we will investigate the so--called alien solutions. %More precisely, we will examine the cases when the above equation implies that %$g(x+y)=g(x)+g(y)$ and $xf(y)+yf(x)=0$. %Concerning this, necessary and sufficient conditions will be provided. Finally, we will discuss the real solutions of the following related functional inequality: $$ g(x+y)-g(x)-g(y)\\geq xf(y)+yf(x). $$"},"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":"1307.0653","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/3.0/","primary_cat":"math.CA","submitted_at":"2013-07-02T10:00:12Z","cross_cats_sorted":[],"title_canon_sha256":"4133703b33735b9d2d0e9128dc03821926016a168dde26312d4dee02a9fa40f1","abstract_canon_sha256":"818855adf7f80a922ebf5a4f33b5ae022915c7ffbaa4a01a815032c76c960eaa"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:19:24.905015Z","signature_b64":"9A/amoEGFJOsEPHoh2lR6ZEeq0pUgk578DvKj/5kEZaJM97i2E9uAsSsQez0DSTiN7HvMhbqt02p1Bc8c9Y/CA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"da4a2a3901ccc13e3ad686e7b3bbdc5ce62df6a5a44ceb01f9bd65cd88fe6f23","last_reissued_at":"2026-05-18T03:19:24.904409Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:19:24.904409Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"General and alien solutions of a functional equation and of a functional inequality","license":"http://creativecommons.org/licenses/by/3.0/","headline":"","cross_cats":[],"primary_cat":"math.CA","authors_text":"Eszter Gselmann, W{\\l}odzimierz Fechner","submitted_at":"2013-07-02T10:00:12Z","abstract_excerpt":"The purpose of the present paper is to solve (under some assumption on the domain) the equation $$ g(x+y)-g(x)-g(y)=xf(y)+yf(x). $$ After determining the general solutions, we will investigate the so--called alien solutions. %More precisely, we will examine the cases when the above equation implies that %$g(x+y)=g(x)+g(y)$ and $xf(y)+yf(x)=0$. %Concerning this, necessary and sufficient conditions will be provided. Finally, we will discuss the real solutions of the following related functional inequality: $$ g(x+y)-g(x)-g(y)\\geq xf(y)+yf(x). $$"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1307.0653","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":"1307.0653","created_at":"2026-05-18T03:19:24.904517+00:00"},{"alias_kind":"arxiv_version","alias_value":"1307.0653v1","created_at":"2026-05-18T03:19:24.904517+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1307.0653","created_at":"2026-05-18T03:19:24.904517+00:00"},{"alias_kind":"pith_short_12","alias_value":"3JFCUOIBZTAT","created_at":"2026-05-18T12:27:32.513160+00:00"},{"alias_kind":"pith_short_16","alias_value":"3JFCUOIBZTAT4OWW","created_at":"2026-05-18T12:27:32.513160+00:00"},{"alias_kind":"pith_short_8","alias_value":"3JFCUOIB","created_at":"2026-05-18T12:27:32.513160+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/3JFCUOIBZTAT4OWWQ3T3HO64LT","json":"https://pith.science/pith/3JFCUOIBZTAT4OWWQ3T3HO64LT.json","graph_json":"https://pith.science/api/pith-number/3JFCUOIBZTAT4OWWQ3T3HO64LT/graph.json","events_json":"https://pith.science/api/pith-number/3JFCUOIBZTAT4OWWQ3T3HO64LT/events.json","paper":"https://pith.science/paper/3JFCUOIB"},"agent_actions":{"view_html":"https://pith.science/pith/3JFCUOIBZTAT4OWWQ3T3HO64LT","download_json":"https://pith.science/pith/3JFCUOIBZTAT4OWWQ3T3HO64LT.json","view_paper":"https://pith.science/paper/3JFCUOIB","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1307.0653&json=true","fetch_graph":"https://pith.science/api/pith-number/3JFCUOIBZTAT4OWWQ3T3HO64LT/graph.json","fetch_events":"https://pith.science/api/pith-number/3JFCUOIBZTAT4OWWQ3T3HO64LT/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/3JFCUOIBZTAT4OWWQ3T3HO64LT/action/timestamp_anchor","attest_storage":"https://pith.science/pith/3JFCUOIBZTAT4OWWQ3T3HO64LT/action/storage_attestation","attest_author":"https://pith.science/pith/3JFCUOIBZTAT4OWWQ3T3HO64LT/action/author_attestation","sign_citation":"https://pith.science/pith/3JFCUOIBZTAT4OWWQ3T3HO64LT/action/citation_signature","submit_replication":"https://pith.science/pith/3JFCUOIBZTAT4OWWQ3T3HO64LT/action/replication_record"}},"created_at":"2026-05-18T03:19:24.904517+00:00","updated_at":"2026-05-18T03:19:24.904517+00:00"}