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In our main result only the continuity of the function $\\varphi$ and a regularity property of the set of zeroes of $f$ are assumed. As application, we determine the solutions of the functional equation $$\n  G(g(u)-g(v))=H(h(u)+h(v))+F(u)+F(v) $$ under monotonicity and differentiability conditions on the unknown functions $F,G,H,g,h$."},"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":"1706.09040","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2017-06-27T20:38:12Z","cross_cats_sorted":[],"title_canon_sha256":"e1a9c7203c347635cafed32c02759f3e12a62c725169c50af3cb49529fd6c901","abstract_canon_sha256":"9eb6a83dac77cb71cb08d64e2284d6e502d7feb2f540f2e91b65f6b3e278cc22"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:23:08.780891Z","signature_b64":"JIo2sw+NOHxGvm2Vns7hqThmD8iDszjLGQH8EO8Af9p8NHMx8RQjPjrXYu8yyRn7t/LgFaHsOCjp2nPzvr7OCw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"21aa728b818a9d6d09f2c3179160ec76f9dee16f024332054ac4c9a978587c8c","last_reissued_at":"2026-05-18T00:23:08.780354Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:23:08.780354Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"On a functional equation related to two-variable weighted quasi-arithmetic means","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CA","authors_text":"Tibor Kiss, Zsolt P\\'ales","submitted_at":"2017-06-27T20:38:12Z","abstract_excerpt":"In this paper, we are going to describe the solutions of the functional equation $$\n  \\varphi\\Big(\\frac{x+y}{2}\\Big)(f(x)+f(y))=\\varphi(x)f(x)+\\varphi(y)f(y) $$ concerning the unknown functions $\\varphi$ and $f$ defined on an open interval. In our main result only the continuity of the function $\\varphi$ and a regularity property of the set of zeroes of $f$ are assumed. As application, we determine the solutions of the functional equation $$\n  G(g(u)-g(v))=H(h(u)+h(v))+F(u)+F(v) $$ under monotonicity and differentiability conditions on the unknown functions $F,G,H,g,h$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1706.09040","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":"1706.09040","created_at":"2026-05-18T00:23:08.780442+00:00"},{"alias_kind":"arxiv_version","alias_value":"1706.09040v1","created_at":"2026-05-18T00:23:08.780442+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1706.09040","created_at":"2026-05-18T00:23:08.780442+00:00"},{"alias_kind":"pith_short_12","alias_value":"EGVHFC4BRKOW","created_at":"2026-05-18T12:31:12.930513+00:00"},{"alias_kind":"pith_short_16","alias_value":"EGVHFC4BRKOW2CPS","created_at":"2026-05-18T12:31:12.930513+00:00"},{"alias_kind":"pith_short_8","alias_value":"EGVHFC4B","created_at":"2026-05-18T12:31:12.930513+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/EGVHFC4BRKOW2CPSYMLZCYHMO3","json":"https://pith.science/pith/EGVHFC4BRKOW2CPSYMLZCYHMO3.json","graph_json":"https://pith.science/api/pith-number/EGVHFC4BRKOW2CPSYMLZCYHMO3/graph.json","events_json":"https://pith.science/api/pith-number/EGVHFC4BRKOW2CPSYMLZCYHMO3/events.json","paper":"https://pith.science/paper/EGVHFC4B"},"agent_actions":{"view_html":"https://pith.science/pith/EGVHFC4BRKOW2CPSYMLZCYHMO3","download_json":"https://pith.science/pith/EGVHFC4BRKOW2CPSYMLZCYHMO3.json","view_paper":"https://pith.science/paper/EGVHFC4B","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1706.09040&json=true","fetch_graph":"https://pith.science/api/pith-number/EGVHFC4BRKOW2CPSYMLZCYHMO3/graph.json","fetch_events":"https://pith.science/api/pith-number/EGVHFC4BRKOW2CPSYMLZCYHMO3/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/EGVHFC4BRKOW2CPSYMLZCYHMO3/action/timestamp_anchor","attest_storage":"https://pith.science/pith/EGVHFC4BRKOW2CPSYMLZCYHMO3/action/storage_attestation","attest_author":"https://pith.science/pith/EGVHFC4BRKOW2CPSYMLZCYHMO3/action/author_attestation","sign_citation":"https://pith.science/pith/EGVHFC4BRKOW2CPSYMLZCYHMO3/action/citation_signature","submit_replication":"https://pith.science/pith/EGVHFC4BRKOW2CPSYMLZCYHMO3/action/replication_record"}},"created_at":"2026-05-18T00:23:08.780442+00:00","updated_at":"2026-05-18T00:23:08.780442+00:00"}