{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,6]],"date-time":"2026-04-06T09:09:27Z","timestamp":1775466567350,"version":"3.50.1"},"reference-count":69,"publisher":"World Scientific Pub Co Pte Ltd","issue":"02","funder":[{"DOI":"10.13039\/501100001659","name":"Deutsche Forschungsgemeinschaft","doi-asserted-by":"crossref","award":["DFG KO 1737\/6-2"],"award-info":[{"award-number":["DFG KO 1737\/6-2"]}],"id":[{"id":"10.13039\/501100001659","id-type":"DOI","asserted-by":"crossref"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["J. Math. Log."],"published-print":{"date-parts":[[2024,8]]},"abstract":"<jats:p> Accretive and monotone operator theory are central branches of nonlinear functional analysis and constitute the abstract study of certain set-valued mappings between function spaces. This paper deals with the computational properties of these accretive and (generalized) monotone set-valued operators. In particular, we develop (and extend) for this field the theoretical framework of proof mining, a program in mathematical logic that seeks to extract computational information from prima facie \u201cnon-computational\u201d proofs from the mainstream literature. To this end, we establish logical metatheorems that guarantee and quantify the computational content of theorems pertaining to accretive and (generalized) monotone set-valued operators. On the one hand, our results unify a number of recent case studies, while they also provide characterizations of central analytical notions in terms of proof theoretic ones on the other, which provides a crucial perspective on needed quantitative assumptions in future applications of proof mining to these branches. <\/jats:p>","DOI":"10.1142\/s0219061323500083","type":"journal-article","created":{"date-parts":[[2023,4,11]],"date-time":"2023-04-11T04:32:26Z","timestamp":1681187546000},"source":"Crossref","is-referenced-by-count":10,"title":["Logical metatheorems for accretive and (generalized) monotone set-valued operators"],"prefix":"10.1142","volume":"24","author":[{"given":"Nicholas","family":"Pischke","sequence":"first","affiliation":[{"name":"Department of Mathematics, Technische Universit\u00e4t Darmstadt, Schlossgartenstra\u00dfe 7, 64289 Darmstadt, Germany"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"219","published-online":{"date-parts":[[2023,5,22]]},"reference":[{"key":"S0219061323500083BIB001","doi-asserted-by":"publisher","DOI":"10.1007\/978-94-010-1537-0"},{"key":"S0219061323500083BIB002","doi-asserted-by":"publisher","DOI":"10.1090\/S0002-9939-02-06528-0"},{"key":"S0219061323500083BIB003","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-319-48311-5"},{"key":"S0219061323500083BIB004","doi-asserted-by":"publisher","DOI":"10.1007\/s11228-011-0187-7"},{"key":"S0219061323500083BIB005","doi-asserted-by":"publisher","DOI":"10.1007\/s10107-020-01500-6"},{"key":"S0219061323500083BIB006","doi-asserted-by":"publisher","DOI":"10.2307\/2274319"},{"key":"S0219061323500083BIB007","doi-asserted-by":"publisher","DOI":"10.1007\/BF02756796"},{"issue":"4","key":"S0219061323500083BIB008","first-page":"459","volume":"3","author":"Bruck R. E.","year":"1977","journal-title":"Houston J. Math."},{"key":"S0219061323500083BIB009","first-page":"1042","volume":"3","author":"Calvert B.","year":"1970","journal-title":"Bollettino Unione Mat. Ital."},{"key":"S0219061323500083BIB010","doi-asserted-by":"publisher","DOI":"10.1137\/S0363012903427336"},{"key":"S0219061323500083BIB011","doi-asserted-by":"publisher","DOI":"10.1090\/S0002-9947-1971-0301592-X"},{"key":"S0219061323500083BIB012","doi-asserted-by":"publisher","DOI":"10.1016\/0022-1236(69)90032-9"},{"key":"S0219061323500083BIB013","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-662-00547-7"},{"key":"S0219061323500083BIB014","doi-asserted-by":"publisher","DOI":"10.4171\/pm\/2054"},{"issue":"3","key":"S0219061323500083BIB015","first-page":"23","volume":"28","author":"Dinis B.","year":"2021","journal-title":"J. Convex Anal."},{"key":"S0219061323500083BIB016","doi-asserted-by":"publisher","DOI":"10.1007\/BF01581204"},{"key":"S0219061323500083BIB017","doi-asserted-by":"publisher","DOI":"10.1016\/j.aim.2019.106728"},{"key":"S0219061323500083BIB018","doi-asserted-by":"publisher","DOI":"10.1016\/j.apal.2004.11.001"},{"key":"S0219061323500083BIB019","doi-asserted-by":"publisher","DOI":"10.1016\/j.jmaa.2005.02.027"},{"key":"S0219061323500083BIB020","doi-asserted-by":"publisher","DOI":"10.1090\/S0002-9947-07-04429-7"},{"key":"S0219061323500083BIB021","first-page":"34","volume":"4","author":"G\u00f6del K.","year":"1933","journal-title":"Ergebnisse eines Mathematischen Kolloquiums"},{"key":"S0219061323500083BIB022","doi-asserted-by":"publisher","DOI":"10.1111\/j.1746-8361.1958.tb01464.x"},{"key":"S0219061323500083BIB023","doi-asserted-by":"publisher","DOI":"10.1016\/j.aim.2015.12.007"},{"key":"S0219061323500083BIB024","series-title":"Lecture Notes in Mathematics","first-page":"454","volume-title":"Metamathematical Investigation of Intuitionistic Arithmetic and Analysis","volume":"344","author":"Howard W. A.","year":"1973"},{"key":"S0219061323500083BIB025","first-page":"479","volume-title":"To H.B. Curry","author":"Howard W. A.","year":"1980"},{"key":"S0219061323500083BIB026","doi-asserted-by":"publisher","DOI":"10.2969\/jmsj\/01940508"},{"key":"S0219061323500083BIB028","doi-asserted-by":"publisher","DOI":"10.2307\/2275367"},{"key":"S0219061323500083BIB029","doi-asserted-by":"publisher","DOI":"10.1007\/BF01794980"},{"key":"S0219061323500083BIB030","doi-asserted-by":"publisher","DOI":"10.1093\/oso\/9780198538622.003.0010"},{"key":"S0219061323500083BIB031","doi-asserted-by":"publisher","DOI":"10.1090\/S0002-9947-04-03515-9"},{"key":"S0219061323500083BIB032","series-title":"Springer Monographs in Mathematics","volume-title":"Applied Proof Theory: Proof Interpretations and their Use in Mathematics","author":"Kohlenbach U.","year":"2008"},{"key":"S0219061323500083BIB033","doi-asserted-by":"publisher","DOI":"10.1007\/s10208-018-9377-0"},{"key":"S0219061323500083BIB034","doi-asserted-by":"publisher","DOI":"10.1142\/9789813272880_0045"},{"issue":"9","key":"S0219061323500083BIB035","first-page":"2125","volume":"21","author":"Kohlenbach U.","year":"2020","journal-title":"J. Nonlinear Convex Anal."},{"issue":"1","key":"S0219061323500083BIB036","first-page":"11","volume":"28","author":"Kohlenbach U.","year":"2021","journal-title":"J. Convex Anal."},{"key":"S0219061323500083BIB037","doi-asserted-by":"publisher","DOI":"10.1007\/s11590-021-01738-9"},{"key":"S0219061323500083BIB038","doi-asserted-by":"publisher","DOI":"10.1016\/j.jmaa.2014.10.035"},{"key":"S0219061323500083BIB039","doi-asserted-by":"publisher","DOI":"10.1098\/rsta.2011.0329"},{"key":"S0219061323500083BIB040","doi-asserted-by":"publisher","DOI":"10.1142\/S0219199717500158"},{"key":"S0219061323500083BIB041","doi-asserted-by":"publisher","DOI":"10.1007\/s11225-016-9702-z"},{"key":"S0219061323500083BIB042","first-page":"136","volume":"242","author":"Kohlenbach U.","year":"2003","journal-title":"Proc. Steklov Inst. Math."},{"key":"S0219061323500083BIB043","first-page":"21","volume":"381","author":"Kohlenbach U.","year":"2023","journal-title":"Philos. Trans. Roy. Soc. A"},{"key":"S0219061323500083BIB044","doi-asserted-by":"publisher","DOI":"10.1016\/j.camwa.2020.04.002"},{"issue":"4","key":"S0219061323500083BIB045","first-page":"241","volume":"16","author":"Kreisel G.","year":"1951","journal-title":"J. Symbol. Logic"},{"key":"S0219061323500083BIB046","doi-asserted-by":"publisher","DOI":"10.2307\/2267457"},{"key":"S0219061323500083BIB047","doi-asserted-by":"publisher","DOI":"10.1017\/S0027763000010023"},{"key":"S0219061323500083BIB048","doi-asserted-by":"publisher","DOI":"10.1016\/j.entcs.2006.05.039"},{"key":"S0219061323500083BIB049","doi-asserted-by":"publisher","DOI":"10.1016\/j.apal.2014.04.015"},{"key":"S0219061323500083BIB050","doi-asserted-by":"publisher","DOI":"10.1007\/s10898-018-0655-9"},{"key":"S0219061323500083BIB051","doi-asserted-by":"publisher","DOI":"10.1007\/s10589-021-00263-w"},{"key":"S0219061323500083BIB052","doi-asserted-by":"publisher","DOI":"10.23952\/jnva.2.2018.2.08"},{"key":"S0219061323500083BIB053","first-page":"154","volume":"4","author":"Martinet B.","year":"1970","journal-title":"Revue fran\u00e7aise d\u2019informatique et de recherche op\u00e9rationnelle"},{"key":"S0219061323500083BIB054","first-page":"194","volume":"257","author":"Minty G. J.","year":"1960","journal-title":"Proc. Roy. Soc. A"},{"key":"S0219061323500083BIB055","doi-asserted-by":"publisher","DOI":"10.1215\/S0012-7094-62-02933-2"},{"key":"S0219061323500083BIB056","doi-asserted-by":"publisher","DOI":"10.1016\/S0898-1221(01)00138-9"},{"key":"S0219061323500083BIB057","doi-asserted-by":"publisher","DOI":"10.1007\/s13370-013-0218-7"},{"key":"S0219061323500083BIB058","doi-asserted-by":"publisher","DOI":"10.1080\/01630563.2021.1876726"},{"issue":"1","key":"S0219061323500083BIB060","first-page":"295","volume":"30","author":"Pischke N.","year":"2023","journal-title":"J. Convex Anal."},{"key":"S0219061323500083BIB061","doi-asserted-by":"publisher","DOI":"10.1137\/0314056"},{"key":"S0219061323500083BIB062","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-642-02431-3"},{"key":"S0219061323500083BIB063","doi-asserted-by":"publisher","DOI":"10.1007\/BF01448013"},{"key":"S0219061323500083BIB064","doi-asserted-by":"publisher","DOI":"10.1137\/0802008"},{"key":"S0219061323500083BIB065","doi-asserted-by":"publisher","DOI":"10.1017\/jsl.2019.55"},{"key":"S0219061323500083BIB066","doi-asserted-by":"publisher","DOI":"10.1007\/s10589-022-00397-5"},{"key":"S0219061323500083BIB067","doi-asserted-by":"publisher","DOI":"10.1090\/pspum\/005\/0154801"},{"key":"S0219061323500083BIB068","volume-title":"Nonlinear Functional Analysis","author":"Takahashi W.","year":"2000"},{"key":"S0219061323500083BIB069","doi-asserted-by":"publisher","DOI":"10.1017\/S0143385708000011"},{"key":"S0219061323500083BIB070","doi-asserted-by":"publisher","DOI":"10.1090\/mbk\/059"},{"key":"S0219061323500083BIB071","doi-asserted-by":"publisher","DOI":"10.1007\/BFb0066739"}],"container-title":["Journal of Mathematical Logic"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.worldscientific.com\/doi\/pdf\/10.1142\/S0219061323500083","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2024,5,6]],"date-time":"2024-05-06T02:26:10Z","timestamp":1714962370000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.worldscientific.com\/doi\/10.1142\/S0219061323500083"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2023,5,22]]},"references-count":69,"journal-issue":{"issue":"02","published-print":{"date-parts":[[2024,8]]}},"alternative-id":["10.1142\/S0219061323500083"],"URL":"https:\/\/doi.org\/10.1142\/s0219061323500083","relation":{},"ISSN":["0219-0613","1793-6691"],"issn-type":[{"value":"0219-0613","type":"print"},{"value":"1793-6691","type":"electronic"}],"subject":[],"published":{"date-parts":[[2023,5,22]]},"article-number":"2350008"}}