{"public_id":"cl_d1321dae528549aee1bea789802f25e5","status":"active","superseded_by_public_id":null,"corpus_id":37655547,"text":"This result generalizes a fixed point theorem for nonexpansive mappings proved independently by F. E. Browder, D. Göhde, and W. A. Kirk.","confidence":0.9,"paper":{"corpus_id":37655547,"title":"A FIXED POINT THEOREM FOR ASYMPTOTICALLY NONEXPANSIVE MAPPINGS","url":"https://sah.borca.ai/papers/37655547"},"contributors":[{"id":32,"public_id":"7c402c1b98","public_label":"뀨 (7c402c1b98)","roles":["extraction"],"url":"https://sah.borca.ai/u/7c402c1b98"},{"id":1,"public_id":"12632b8b5f","public_label":"Anonymous (12632b8b5f)","roles":["review"],"url":"https://sah.borca.ai/u/12632b8b5f"}],"origin_summary":{"object_type":"claim","status":"active","confidence":0.9,"origin_kinds":["extraction","extraction_create"],"contribution_count":1,"contribution_task_types":["extraction"],"contribution_statuses":["applied"],"verifier_verdict_count":2,"verifier_classes":["system"],"verifier_class_counts":{"system":2,"user_agent":0},"verdict_counts":{"approve":1,"reject":1},"verifier_state":"system_only","basis":["kg_settlement_results.decision_payload.legacy_bridge","kg_entity_origin_refs","kg_assertion_proposals","contributions","verifications","claim.status","claim.confidence"],"limits":["ledger provenance is aggregated; raw contribution and verifier audit rows are not expanded","entity matching uses settlement bridge refs and edge commands"]},"concepts":[{"public_id":"co_2987dc6f32c685d8dccc060e4d8d3bde","name":"asymptotically nonexpansive mapping","description":"A mapping F: K → K such that there exists a sequence {k_i} of real numbers with k_i → 1 as i → ∞ and ‖F^i x − F^i y‖ ≤ k_i ‖x − y‖ for all x, y ∈ K.","types":["mapping","mathematical concept"],"url":"https://sah.borca.ai/concepts/co_2987dc6f32c685d8dccc060e4d8d3bde"},{"public_id":"co_59ca8d90b9cb2df631515b04d4286da5","name":"fixed point","description":"A point x ∈ K such that F(x) = x, whose existence is proved under the stated conditions.","types":["mathematical object"],"url":"https://sah.borca.ai/concepts/co_59ca8d90b9cb2df631515b04d4286da5"},{"public_id":"co_d3487ee9dedd527576e17732543587e7","name":"nonexpansive mapping","description":"A mapping F: K → K satisfying ‖F x − F y‖ ≤ ‖x − y‖ for all x, y ∈ K, whose fixed point theorem is generalized by the present result.","types":["mapping","mathematical concept"],"url":"https://sah.borca.ai/concepts/co_d3487ee9dedd527576e17732543587e7"}],"related_claims":[],"url":"https://sah.borca.ai/claims/cl_d1321dae528549aee1bea789802f25e5"}