{"id":"W2122615076","doi":"10.1090/s0002-9939-06-08770-3","title":"Fenchel duality, Fitzpatrick functions and the extension of firmly nonexpansive mappings","year":2006,"lang":"en","type":"article","venue":"Proceedings of the American Mathematical Society","topic":"Optimization and Variational Analysis","field":"Computer Science","cited_by":26,"is_retracted":false,"has_abstract":true,"ca_institutions":"Okanagan University College; University of British Columbia, Okanagan Campus; University of British Columbia","funders":"Natural Sciences and Engineering Research Council of Canada","keywords":"Extension (predicate logic); Duality (order theory); Mathematics; Pure mathematics; Computer science","routes":{"ca_aff":true,"ca_fund":true,"ca_venue":false,"about_ca":false,"invisible_to_affiliation_only":false},"retraction":null,"screen":null,"direct_labels":[],"prediction":{"model_version":"codex-gemma-dda1882f352a","candidate_categories":[],"consensus_categories":[],"category_scores_codex":[0.000491034,0.00009839147,0.0002934961,0.00002331854,0.0001745698,0.00005456299,0.0004280331,0.00002511237,0.00000920524],"category_scores_gemma":[0.000204392,0.00005271968,0.0002737538,0.0009305984,0.0006413501,0.0001565325,0.0003340476,0.00009162584,0.000002789484],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.00001722276,"about_ca_system_score_gemma":0.000019908,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.0001128787,"about_ca_topic_score_gemma":3.489299e-7,"domain_scores_codex":[0.9989468,0.00001507438,0.0003448878,0.0001913571,0.0003797253,0.0001221041],"domain_scores_gemma":[0.9985615,0.0002804812,0.000547979,0.0001555274,0.0004243466,0.00003014099],"domain_codex":null,"domain_gemma":null,"domain_candidate":null,"domain_consensus":null,"study_design_codex":"theoretical_or_conceptual","study_design_gemma":"simulation_or_modeling","study_design_scores_codex":[0.00001895822,0.0002461973,0.002842568,0.0001634662,0.0001480151,4.111079e-8,0.003073758,0.000258773,0.003139329,0.9803455,0.009067002,0.0006963918],"study_design_scores_gemma":[0.0009288824,0.00007064748,0.03290816,0.00007769677,0.0002393167,0.00001554476,0.002941527,0.5835473,0.001329435,0.3774914,0.0002002988,0.0002498181],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":null,"genre_codex":"methods","genre_gemma":"empirical","genre_scores_codex":[0.4690146,0.0001133001,0.47108,0.05090768,0.00006101676,0.0006187409,0.00001239723,0.0001080713,0.008084132],"genre_scores_gemma":[0.9291348,0.00002645782,0.06955181,0.0006580942,0.00003223324,0.00001331156,5.822574e-7,0.000005743066,0.0005769499],"genre_candidate":"empirical","genre_consensus":null,"teacher_disagreement_score":0.6028541,"threshold_uncertainty_score":0.2363081,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.007859103356037676,"score_gpt":0.2202212309377909,"score_spread":0.2123621275817532,"validation_status":"score_only:v0-immature-baseline","note":"Baseline scores from an immature model (maturity gate not passed). Scores rank; they never assert a category."}}