{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,28]],"date-time":"2026-04-28T05:19:47Z","timestamp":1777353587860,"version":"3.51.4"},"reference-count":25,"publisher":"Cambridge University Press (CUP)","issue":"1","license":[{"start":{"date-parts":[[2013,5,13]],"date-time":"2013-05-13T00:00:00Z","timestamp":1368403200000},"content-version":"unspecified","delay-in-days":0,"URL":"https:\/\/www.cambridge.org\/core\/terms"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Math. Struct. Comp. Sci."],"published-print":{"date-parts":[[2014,2]]},"abstract":"<jats:p>In this paper we study approach structures on dcpo's. A dcpo (<jats:italic>X<\/jats:italic>, \u2264) will be endowed with several other structures: the Scott topology; an approach structure generated by a collection of weightable quasi metrics on<jats:italic>X<\/jats:italic>; and a collection<jats:private-char><jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" mime-subtype=\"gif\" mimetype=\"image\" xlink:type=\"simple\" xlink:href=\"S0960129513000017_char1\"\/><\/jats:private-char>of weights corresponding to the quasi metrics. Understanding the interaction between these structures on<jats:italic>X<\/jats:italic>will eventually lead to some fixed-point theorems for the morphisms in the category of approach spaces, which are called contractions. Existing fixed-point theorems on both monotone and non-monotone maps are obtained as special cases.<\/jats:p>","DOI":"10.1017\/s0960129513000017","type":"journal-article","created":{"date-parts":[[2013,5,13]],"date-time":"2013-05-13T09:04:18Z","timestamp":1368435858000},"source":"Crossref","is-referenced-by-count":9,"title":["Fixed points of contractive maps on dcpo's"],"prefix":"10.1017","volume":"24","author":[{"given":"E.","family":"COLEBUNDERS","sequence":"first","affiliation":[]},{"given":"S.","family":"DE WACHTER","sequence":"additional","affiliation":[]},{"given":"R.","family":"LOWEN","sequence":"additional","affiliation":[]}],"member":"56","published-online":{"date-parts":[[2013,5,13]]},"reference":[{"key":"S0960129513000017_ref17","first-page":"17","article-title":"Banach's fixed point theorem for partial metric spaces.","volume":"36","author":"Oltra","year":"2004","journal-title":"Rendiconti dell'Istituto di Matematica dell'Universit di Trieste"},{"key":"S0960129513000017_ref11","doi-asserted-by":"publisher","DOI":"10.1007\/978-94-017-0470-0_3"},{"key":"S0960129513000017_ref6","doi-asserted-by":"publisher","DOI":"10.1016\/S0304-3975(96)00243-5"},{"key":"S0960129513000017_ref8","doi-asserted-by":"publisher","DOI":"10.1017\/CBO9780511542725"},{"key":"S0960129513000017_ref9","doi-asserted-by":"crossref","unstructured":"Gutierres G. and Hofmann D. (2012) Approaching metric domains. Applied Categorical Structures.","DOI":"10.1007\/s10485-011-9274-z"},{"key":"S0960129513000017_ref5","doi-asserted-by":"publisher","DOI":"10.1007\/978-94-015-8400-5"},{"key":"S0960129513000017_ref24","doi-asserted-by":"publisher","DOI":"10.1016\/S1571-0661(04)80975-7"},{"key":"S0960129513000017_ref7","doi-asserted-by":"publisher","DOI":"10.1016\/j.jmaa.2008.07.026"},{"key":"S0960129513000017_ref13","doi-asserted-by":"crossref","DOI":"10.1093\/oso\/9780198500308.001.0001","volume-title":"Approach spaces","author":"Lowen","year":"1997"},{"key":"S0960129513000017_ref15","doi-asserted-by":"publisher","DOI":"10.1007\/3-540-45022-X_11"},{"key":"S0960129513000017_ref1","volume-title":"Abstract and concrete categories","author":"Ad\u00e1mek","year":"1990"},{"key":"S0960129513000017_ref22","doi-asserted-by":"publisher","DOI":"10.1016\/S0304-3975(02)00705-3"},{"key":"S0960129513000017_ref23","first-page":"97","article-title":"Continuous lattices.","volume":"274","author":"Scott","year":"1972","journal-title":"Springer-Verlag Lecture Notes in Computer Science"},{"key":"S0960129513000017_ref4","first-page":"1","article-title":"Complexity analysis via approach spaces.","volume":"20","author":"Colebunders","year":"2012","journal-title":"Applied Categorical Structures"},{"key":"S0960129513000017_ref3","doi-asserted-by":"publisher","DOI":"10.1016\/j.topol.2011.01.025"},{"key":"S0960129513000017_ref18","doi-asserted-by":"publisher","DOI":"10.1016\/S0166-8641(98)00102-3"},{"key":"S0960129513000017_ref21","doi-asserted-by":"publisher","DOI":"10.1016\/S1571-0661(04)00029-5"},{"key":"S0960129513000017_ref19","doi-asserted-by":"publisher","DOI":"10.1016\/j.topol.2011.01.005"},{"key":"S0960129513000017_ref14","unstructured":"Martin K. (2000a) A foundation for computation, Ph.D. thesis, Tulane University."},{"key":"S0960129513000017_ref2","doi-asserted-by":"publisher","DOI":"10.1016\/j.jmaa.2010.09.006"},{"key":"S0960129513000017_ref10","doi-asserted-by":"publisher","DOI":"10.1023\/A:1008684018933"},{"key":"S0960129513000017_ref12","doi-asserted-by":"publisher","DOI":"10.1111\/j.1749-6632.1994.tb44134.x"},{"key":"S0960129513000017_ref16","doi-asserted-by":"publisher","DOI":"10.1111\/j.1749-6632.1994.tb44144.x"},{"key":"S0960129513000017_ref20","first-page":"481","volume-title":"Categorical topology \u2013 Proceedings Conference Toledo, Ohio 1983","author":"Salbany","year":"1984"},{"key":"S0960129513000017_ref25","doi-asserted-by":"publisher","DOI":"10.1023\/A:1023012924892"}],"container-title":["Mathematical Structures in Computer Science"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.cambridge.org\/core\/services\/aop-cambridge-core\/content\/view\/S0960129513000017","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2024,5,10]],"date-time":"2024-05-10T16:10:56Z","timestamp":1715357456000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.cambridge.org\/core\/product\/identifier\/S0960129513000017\/type\/journal_article"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2013,5,13]]},"references-count":25,"journal-issue":{"issue":"1","published-print":{"date-parts":[[2014,2]]}},"alternative-id":["S0960129513000017"],"URL":"https:\/\/doi.org\/10.1017\/s0960129513000017","relation":{},"ISSN":["0960-1295","1469-8072"],"issn-type":[{"value":"0960-1295","type":"print"},{"value":"1469-8072","type":"electronic"}],"subject":[],"published":{"date-parts":[[2013,5,13]]},"article-number":"e240102"}}