{"id":"https://openalex.org/W2087720105","doi":"https://doi.org/10.1155/2014/892641","title":"Implicit Multifunction Theorems in Banach Spaces","display_name":"Implicit Multifunction Theorems in Banach Spaces","publication_year":2014,"publication_date":"2014-01-01","ids":{"openalex":"https://openalex.org/W2087720105","doi":"https://doi.org/10.1155/2014/892641","mag":"2087720105"},"language":"en","primary_location":{"id":"doi:10.1155/2014/892641","is_oa":true,"landing_page_url":"https://doi.org/10.1155/2014/892641","pdf_url":"https://downloads.hindawi.com/journals/jam/2014/892641.pdf","source":{"id":"https://openalex.org/S190082376","display_name":"Journal of Applied Mathematics","issn_l":"1110-757X","issn":["1110-757X","1687-0042"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310319869","host_organization_name":"Hindawi Publishing Corporation","host_organization_lineage":["https://openalex.org/P4310319869","https://openalex.org/P4310320595"],"host_organization_lineage_names":["Hindawi Publishing Corporation","Wiley"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of Applied Mathematics","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","doaj"],"open_access":{"is_oa":true,"oa_status":"gold","oa_url":"https://downloads.hindawi.com/journals/jam/2014/892641.pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5081735562","display_name":"Ming-ge Yang","orcid":null},"institutions":[{"id":"https://openalex.org/I24943067","display_name":"Fudan University","ror":"https://ror.org/013q1eq08","country_code":"CN","type":"education","lineage":["https://openalex.org/I24943067"]},{"id":"https://openalex.org/I4210117164","display_name":"Luoyang Normal University","ror":"https://ror.org/029man787","country_code":"CN","type":"education","lineage":["https://openalex.org/I4210117164"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"Ming-ge Yang","raw_affiliation_strings":["Department of Mathematics, Luoyang Normal University, Luoyang, Henan 471022, China","School of Management, Fudan University, Shanghai 200433, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Luoyang Normal University, Luoyang, Henan 471022, China","institution_ids":["https://openalex.org/I4210117164"]},{"raw_affiliation_string":"School of Management, Fudan University, Shanghai 200433, China","institution_ids":["https://openalex.org/I24943067"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5103166791","display_name":"Yifan Xu","orcid":"https://orcid.org/0000-0003-2467-888X"},"institutions":[{"id":"https://openalex.org/I24943067","display_name":"Fudan University","ror":"https://ror.org/013q1eq08","country_code":"CN","type":"education","lineage":["https://openalex.org/I24943067"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Yi-fan Xu","raw_affiliation_strings":["School of Management, Fudan University, Shanghai 200433, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Management, Fudan University, Shanghai 200433, China","institution_ids":["https://openalex.org/I24943067"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5081735562"],"corresponding_institution_ids":["https://openalex.org/I24943067","https://openalex.org/I4210117164"],"apc_list":{"value":1130,"currency":"USD","value_usd":1130},"apc_paid":{"value":1130,"currency":"USD","value_usd":1130},"fwci":0.0,"has_fulltext":true,"cited_by_count":0,"citation_normalized_percentile":{"value":0.129113,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"2014","issue":null,"first_page":"1","last_page":"7"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10545","display_name":"Optimization and Variational Analysis","score":0.9998000264167786,"subfield":{"id":"https://openalex.org/subfields/1703","display_name":"Computational Theory and Mathematics"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T10545","display_name":"Optimization and Variational Analysis","score":0.9998000264167786,"subfield":{"id":"https://openalex.org/subfields/1703","display_name":"Computational Theory and Mathematics"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T12809","display_name":"Contact Mechanics and Variational Inequalities","score":0.9987999796867371,"subfield":{"id":"https://openalex.org/subfields/1703","display_name":"Computational Theory and Mathematics"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T11777","display_name":"Fixed Point Theorems Analysis","score":0.9958000183105469,"subfield":{"id":"https://openalex.org/subfields/2608","display_name":"Geometry and Topology"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.8417384028434753},{"id":"https://openalex.org/keywords/banach-space","display_name":"Banach space","score":0.7161245346069336},{"id":"https://openalex.org/keywords/lipschitz-continuity","display_name":"Lipschitz continuity","score":0.7028542160987854},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.6046854853630066},{"id":"https://openalex.org/keywords/property","display_name":"Property (philosophy)","score":0.5194677710533142},{"id":"https://openalex.org/keywords/metric","display_name":"Metric (unit)","score":0.5144789218902588},{"id":"https://openalex.org/keywords/metric-space","display_name":"Metric space","score":0.4859720468521118},{"id":"https://openalex.org/keywords/subderivative","display_name":"Subderivative","score":0.4812164604663849},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.3218393325805664},{"id":"https://openalex.org/keywords/regular-polygon","display_name":"Regular polygon","score":0.24949723482131958},{"id":"https://openalex.org/keywords/convex-optimization","display_name":"Convex optimization","score":0.053786784410476685},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.04333195090293884}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8417384028434753},{"id":"https://openalex.org/C132954091","wikidata":"https://www.wikidata.org/wiki/Q194397","display_name":"Banach space","level":2,"score":0.7161245346069336},{"id":"https://openalex.org/C22324862","wikidata":"https://www.wikidata.org/wiki/Q652707","display_name":"Lipschitz continuity","level":2,"score":0.7028542160987854},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.6046854853630066},{"id":"https://openalex.org/C189950617","wikidata":"https://www.wikidata.org/wiki/Q937228","display_name":"Property (philosophy)","level":2,"score":0.5194677710533142},{"id":"https://openalex.org/C176217482","wikidata":"https://www.wikidata.org/wiki/Q860554","display_name":"Metric (unit)","level":2,"score":0.5144789218902588},{"id":"https://openalex.org/C198043062","wikidata":"https://www.wikidata.org/wiki/Q180953","display_name":"Metric space","level":2,"score":0.4859720468521118},{"id":"https://openalex.org/C200661725","wikidata":"https://www.wikidata.org/wiki/Q289500","display_name":"Subderivative","level":4,"score":0.4812164604663849},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.3218393325805664},{"id":"https://openalex.org/C112680207","wikidata":"https://www.wikidata.org/wiki/Q714886","display_name":"Regular polygon","level":2,"score":0.24949723482131958},{"id":"https://openalex.org/C157972887","wikidata":"https://www.wikidata.org/wiki/Q463359","display_name":"Convex optimization","level":3,"score":0.053786784410476685},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.04333195090293884},{"id":"https://openalex.org/C111472728","wikidata":"https://www.wikidata.org/wiki/Q9471","display_name":"Epistemology","level":1,"score":0.0},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.0},{"id":"https://openalex.org/C138885662","wikidata":"https://www.wikidata.org/wiki/Q5891","display_name":"Philosophy","level":0,"score":0.0},{"id":"https://openalex.org/C21547014","wikidata":"https://www.wikidata.org/wiki/Q1423657","display_name":"Operations management","level":1,"score":0.0}],"mesh":[],"locations_count":4,"locations":[{"id":"doi:10.1155/2014/892641","is_oa":true,"landing_page_url":"https://doi.org/10.1155/2014/892641","pdf_url":"https://downloads.hindawi.com/journals/jam/2014/892641.pdf","source":{"id":"https://openalex.org/S190082376","display_name":"Journal of Applied Mathematics","issn_l":"1110-757X","issn":["1110-757X","1687-0042"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310319869","host_organization_name":"Hindawi Publishing Corporation","host_organization_lineage":["https://openalex.org/P4310319869","https://openalex.org/P4310320595"],"host_organization_lineage_names":["Hindawi Publishing Corporation","Wiley"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of Applied Mathematics","raw_type":"journal-article"},{"id":"pmh:oai:CULeuclid:euclid.jam/1412177579","is_oa":false,"landing_page_url":"http://projecteuclid.org/euclid.jam/1412177579","pdf_url":null,"source":{"id":"https://openalex.org/S4306400787","display_name":"Project Euclid (Cornell University)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"Text"},{"id":"pmh:oai:RePEc:hin:jnljam:892641","is_oa":false,"landing_page_url":"http://downloads.hindawi.com/journals/JAM/2014/892641.xml","pdf_url":null,"source":{"id":"https://openalex.org/S4306401271","display_name":"RePEc: Research Papers in Economics","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I77793887","host_organization_name":"Federal Reserve Bank of St. Louis","host_organization_lineage":["https://openalex.org/I77793887"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"article"},{"id":"pmh:oai:doaj.org/article:f32346eb1b084f55bf676ca9e1943ce8","is_oa":true,"landing_page_url":"https://doaj.org/article/f32346eb1b084f55bf676ca9e1943ce8","pdf_url":null,"source":{"id":"https://openalex.org/S4306401280","display_name":"DOAJ (DOAJ: Directory of Open Access Journals)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by-sa","license_id":"https://openalex.org/licenses/cc-by-sa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Journal of Applied Mathematics, Vol 2014 (2014)","raw_type":"article"}],"best_oa_location":{"id":"doi:10.1155/2014/892641","is_oa":true,"landing_page_url":"https://doi.org/10.1155/2014/892641","pdf_url":"https://downloads.hindawi.com/journals/jam/2014/892641.pdf","source":{"id":"https://openalex.org/S190082376","display_name":"Journal of Applied Mathematics","issn_l":"1110-757X","issn":["1110-757X","1687-0042"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310319869","host_organization_name":"Hindawi Publishing Corporation","host_organization_lineage":["https://openalex.org/P4310319869","https://openalex.org/P4310320595"],"host_organization_lineage_names":["Hindawi Publishing Corporation","Wiley"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of Applied Mathematics","raw_type":"journal-article"},"sustainable_development_goals":[{"id":"https://metadata.un.org/sdg/10","score":0.5899999737739563,"display_name":"Reduced inequalities"}],"awards":[{"id":"https://openalex.org/G1320829102","display_name":null,"funder_award_id":"2011B110025","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G2885696694","display_name":null,"funder_award_id":"11226228","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G3191873539","display_name":null,"funder_award_id":"11301254","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G3738233063","display_name":"\u57fa\u4e8e\u987e\u5ba2\u884c\u4e3a\u4e0e\u6e20\u9053\u7ade\u4e89\u7684\u6536\u76ca\u7ba1\u7406\u95ee\u9898\u7814\u7a76","funder_award_id":"71372113","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G559240246","display_name":null,"funder_award_id":"122300410256","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"}],"funders":[{"id":"https://openalex.org/F4320321001","display_name":"National Natural Science Foundation of China","ror":"https://ror.org/01h0zpd94"}],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2087720105.pdf","grobid_xml":"https://content.openalex.org/works/W2087720105.grobid-xml"},"referenced_works_count":18,"referenced_works":["https://openalex.org/W185728265","https://openalex.org/W1522222833","https://openalex.org/W1528330203","https://openalex.org/W1737349770","https://openalex.org/W1868077198","https://openalex.org/W1964590033","https://openalex.org/W1989701997","https://openalex.org/W1997348293","https://openalex.org/W2018508199","https://openalex.org/W2055989000","https://openalex.org/W2069184934","https://openalex.org/W2070606259","https://openalex.org/W2072522538","https://openalex.org/W2094683072","https://openalex.org/W2153562582","https://openalex.org/W2798813531","https://openalex.org/W4254302264","https://openalex.org/W4285719527"],"related_works":["https://openalex.org/W3185235544","https://openalex.org/W2911623553","https://openalex.org/W4297791327","https://openalex.org/W2897842840","https://openalex.org/W2397777611","https://openalex.org/W2072255091","https://openalex.org/W2761731838","https://openalex.org/W4298179680","https://openalex.org/W2084754442","https://openalex.org/W4297851895"],"abstract_inverted_index":{"This":[0],"paper":[1],"is":[2],"mainly":[3],"devoted":[4],"to":[5],"the":[6,27,53,57,61],"study":[7],"of":[8,14,39,49],"implicit":[9,40],"multifunction":[10],"theorems":[11],"in":[12,17,42],"terms":[13],"Clarke":[15,58,62],"coderivative":[16],"general":[18,43],"Banach":[19,44],"spaces.":[20,45],"We":[21],"present":[22],"new":[23],"sufficient":[24],"conditions":[25],"for":[26],"local":[28],"metric":[29,31],"regularity,":[30,32],"Lipschitz-like":[33],"property,":[34],"nonemptiness,":[35],"and":[36,60],"lower":[37],"semicontinuity":[38],"multifunctions":[41],"The":[46],"basic":[47],"tools":[48],"our":[50],"analysis":[51],"involve":[52],"Ekeland":[54],"variational":[55],"principle,":[56],"subdifferential,":[59],"coderivative.":[63]},"counts_by_year":[],"updated_date":"2026-08-21T09:56:20.448147","created_date":"2025-10-10T00:00:00"}