{"id":{"repo_id":"unt","oai_identifier":"info:ark/67531/metadc4971"},"canonical_url":"https://search.dev.ndltd.org/etd/unt/info:ark/67531/metadc4971","repository":{"repo_id":"unt","name":"University of North Texas","base_url":"https://digital.library.unt.edu/oai/"},"display":{"title":"Applications in Fixed Point Theory","abstract":"Banach's contraction principle is probably one of the most important theorems in fixed point theory. It has been used to develop much of the rest of fixed point theory. Another key result in the field is a theorem due to Browder, Göhde, and Kirk involving Hilbert spaces and nonexpansive mappings. Several applications of Banach's contraction principle are made. Some of these applications involve obtaining new metrics on a space, forcing a continuous map to have a fixed point, and using conditions on the boundary of a closed ball in a Banach space to obtain a fixed point. Finally, a development of the theorem due to Browder et al. is given with Hilbert spaces replaced by uniformly convex Banach spaces.","abstract_html":"Banach's contraction principle is probably one of the most important theorems in fixed point theory. It has been used to develop much of the rest of fixed point theory. Another key result in the field is a theorem due to Browder, Göhde, and Kirk involving Hilbert spaces and nonexpansive mappings. Several applications of Banach's contraction principle are made. Some of these applications involve obtaining new metrics on a space, forcing a continuous map to have a fixed point, and using conditions on the boundary of a closed ball in a Banach space to obtain a fixed point. Finally, a development of the theorem due to Browder et al. is given with Hilbert spaces replaced by uniformly convex Banach spaces.","abstract_has_math":false,"creators":["Farmer, Matthew Ray"],"institution":"University of North Texas","degree_name":null,"degree_level":null,"degree_discipline":null,"degree_department":null,"school":null,"contributors":["Bator, Elizabeth M.","Lewis, Paul","Jackson, Stephen C."],"advisors":[],"committee_chairs":[],"committee_members":[],"year":2005,"date_issued":"2005-12","date_published":"2005-12","updated_at":"2026-07-24T05:35:09Z","subjects":["Fixed point theory.","Banach spaces.","metric space","non-expansive maps","contraction maps","fixed points","Hilbert spaces"],"languages":["English"],"rights":["Public","Copyright","Farmer, Matthew Ray","Copyright is held by the author, unless otherwise noted. All rights reserved."],"rights_urls":[],"identifier_entries":[{"key":"dc:identifier","label":"Identifier","values":["oclc: 68903182","https://digital.library.unt.edu/ark:/67531/metadc4971/","ark: ark:/67531/metadc4971"],"render_values":[{"text":"oclc: 68903182","href":null,"code":true},{"text":"https://digital.library.unt.edu/ark:/67531/metadc4971/","href":"https://digital.library.unt.edu/ark:/67531/metadc4971/","code":true},{"text":"ark: ark:/67531/metadc4971","href":null,"code":true}]}]},"links":{"outbound_url":"https://doi.org/10.12794/metadc4971","outbound_label":"DOI","outbound_source":"dc:identifier"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:contributor","label":"Contributor","values":["Bator, Elizabeth M.","Lewis, Paul","Jackson, Stephen C."]},{"key":"dc:creator","label":"Author","values":["Farmer, Matthew Ray"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date","label":"Dc Date","values":["2005-12"]},{"key":"dc:publisher","label":"Institution","values":["University of North Texas"]},{"key":"dc:type","label":"Dc Type","values":["Thesis or Dissertation"]}]},{"id":"subjects_keywords","label":"Subjects and Keywords","entries":[{"key":"dc:subject","label":"Dc Subject","values":["Fixed point theory.","Banach spaces.","metric space","non-expansive maps","contraction maps","fixed points","Hilbert spaces"]}]},{"id":"language_rights","label":"Language and Rights","entries":[{"key":"dc:language","label":"Dc Language","values":["English"]},{"key":"dc:rights","label":"Dc Rights","values":["Public","Copyright","Farmer, Matthew Ray","Copyright is held by the author, unless otherwise noted. 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Finally, a development of the theorem due to Browder et al. is given with Hilbert spaces replaced by uniformly convex Banach spaces."]},{"key":"dc:format","label":"Dc Format","values":["Text"]},{"key":"dc:title","label":"Title","values":["Applications in Fixed Point Theory"]}]}],"canonical_facts":{"dc:contributor":["Bator, Elizabeth M.","Lewis, Paul","Jackson, Stephen C."],"dc:creator":["Farmer, Matthew Ray"],"dc:date":["2005-12"],"dc:description":["Banach's contraction principle is probably one of the most important theorems in fixed point theory. It has been used to develop much of the rest of fixed point theory. Another key result in the field is a theorem due to Browder, Göhde, and Kirk involving Hilbert spaces and nonexpansive mappings. Several applications of Banach's contraction principle are made. Some of these applications involve obtaining new metrics on a space, forcing a continuous map to have a fixed point, and using conditions on the boundary of a closed ball in a Banach space to obtain a fixed point. Finally, a development of the theorem due to Browder et al. is given with Hilbert spaces replaced by uniformly convex Banach spaces."],"dc:format":["Text"],"dc:identifier":["oclc: 68903182","doi: 10.12794/metadc4971","https://digital.library.unt.edu/ark:/67531/metadc4971/","ark: ark:/67531/metadc4971"],"dc:language":["English"],"dc:publisher":["University of North Texas"],"dc:rights":["Public","Copyright","Farmer, Matthew Ray","Copyright is held by the author, unless otherwise noted. All rights reserved."],"dc:subject":["Fixed point theory.","Banach spaces.","metric space","non-expansive maps","contraction maps","fixed points","Hilbert spaces"],"dc:title":["Applications in Fixed Point Theory"],"dc:type":["Thesis or Dissertation"]},"updated_at":"2026-07-24T05:35:09Z"}