{"id":"https://openalex.org/W2036053795","doi":"https://doi.org/10.1155/2012/580158","title":"Algorithms for a System of General Variational Inequalities in Banach Spaces","display_name":"Algorithms for a System of General Variational Inequalities in Banach Spaces","publication_year":2012,"publication_date":"2012-01-01","ids":{"openalex":"https://openalex.org/W2036053795","doi":"https://doi.org/10.1155/2012/580158","mag":"2036053795"},"language":"en","primary_location":{"id":"doi:10.1155/2012/580158","is_oa":true,"landing_page_url":"https://doi.org/10.1155/2012/580158","pdf_url":"https://downloads.hindawi.com/journals/jam/2012/580158.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"],"host_organization_lineage_names":["Hindawi Publishing Corporation"],"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/2012/580158.pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5100864866","display_name":"Jinhua Zhu","orcid":null},"institutions":[{"id":"https://openalex.org/I4210131342","display_name":"Yibin University","ror":"https://ror.org/03w8m2977","country_code":"CN","type":"education","lineage":["https://openalex.org/I4210131342"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Jin-Hua Zhu","raw_affiliation_strings":["Department of Mathematics, Yibin University, Sichuan, Yibin 644007, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Yibin University, Sichuan, Yibin 644007, China","institution_ids":["https://openalex.org/I4210131342"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5102157579","display_name":"Shih-sen Chang","orcid":null},"institutions":[{"id":"https://openalex.org/I49185572","display_name":"Yunnan University of Finance And Economics","ror":"https://ror.org/04rhev598","country_code":"CN","type":"education","lineage":["https://openalex.org/I49185572"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Shih-Sen Chang","raw_affiliation_strings":["College of Statistics and Mathematics, Yunnan University of Finance and Economics, Yunnan, Kunming 650221, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"College of Statistics and Mathematics, Yunnan University of Finance and Economics, Yunnan, Kunming 650221, China","institution_ids":["https://openalex.org/I49185572"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5103252847","display_name":"Min Liu","orcid":"https://orcid.org/0000-0002-9905-6877"},"institutions":[{"id":"https://openalex.org/I4210131342","display_name":"Yibin University","ror":"https://ror.org/03w8m2977","country_code":"CN","type":"education","lineage":["https://openalex.org/I4210131342"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Min Liu","raw_affiliation_strings":["Department of Mathematics, Yibin University, Sichuan, Yibin 644007, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Yibin University, Sichuan, Yibin 644007, China","institution_ids":["https://openalex.org/I4210131342"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":{"value":1025,"currency":"USD","value_usd":1025},"apc_paid":{"value":1025,"currency":"USD","value_usd":1025},"fwci":0.34,"has_fulltext":true,"cited_by_count":2,"citation_normalized_percentile":{"value":0.61465545,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":94},"biblio":{"volume":"2012","issue":"1","first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10545","display_name":"Optimization and Variational Analysis","score":0.9998999834060669,"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":0.9998999834060669,"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":0.9940999746322632,"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":0.9840999841690063,"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":0.8287676572799683},{"id":"https://openalex.org/keywords/variational-inequality","display_name":"Variational inequality","score":0.781562089920044},{"id":"https://openalex.org/keywords/banach-space","display_name":"Banach space","score":0.7805636525154114},{"id":"https://openalex.org/keywords/class","display_name":"Class (philosophy)","score":0.6710940599441528},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.5496309399604797},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.47271913290023804},{"id":"https://openalex.org/keywords/inequality","display_name":"Inequality","score":0.45318102836608887},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.4098570644855499},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.3220897912979126},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.10016846656799316}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8287676572799683},{"id":"https://openalex.org/C161999928","wikidata":"https://www.wikidata.org/wiki/Q4556320","display_name":"Variational inequality","level":2,"score":0.781562089920044},{"id":"https://openalex.org/C132954091","wikidata":"https://www.wikidata.org/wiki/Q194397","display_name":"Banach space","level":2,"score":0.7805636525154114},{"id":"https://openalex.org/C2777212361","wikidata":"https://www.wikidata.org/wiki/Q5127848","display_name":"Class (philosophy)","level":2,"score":0.6710940599441528},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.5496309399604797},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.47271913290023804},{"id":"https://openalex.org/C45555294","wikidata":"https://www.wikidata.org/wiki/Q28113351","display_name":"Inequality","level":2,"score":0.45318102836608887},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.4098570644855499},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.3220897912979126},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.10016846656799316},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.0},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0}],"mesh":[],"locations_count":4,"locations":[{"id":"doi:10.1155/2012/580158","is_oa":true,"landing_page_url":"https://doi.org/10.1155/2012/580158","pdf_url":"https://downloads.hindawi.com/journals/jam/2012/580158.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"],"host_organization_lineage_names":["Hindawi Publishing Corporation"],"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/1357179978","is_oa":false,"landing_page_url":"http://projecteuclid.org/euclid.jam/1357179978","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:580158","is_oa":false,"landing_page_url":"http://downloads.hindawi.com/journals/JAM/2012/580158.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:4cf0b165a2e849d3b50ca69e19b2e776","is_oa":true,"landing_page_url":"https://doaj.org/article/4cf0b165a2e849d3b50ca69e19b2e776","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 2012 (2012)","raw_type":"article"}],"best_oa_location":{"id":"doi:10.1155/2012/580158","is_oa":true,"landing_page_url":"https://doi.org/10.1155/2012/580158","pdf_url":"https://downloads.hindawi.com/journals/jam/2012/580158.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"],"host_organization_lineage_names":["Hindawi Publishing Corporation"],"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":[{"display_name":"Reduced inequalities","id":"https://metadata.un.org/sdg/10","score":0.6399999856948853}],"awards":[{"id":"https://openalex.org/G2539603941","display_name":null,"funder_award_id":"11ZB146","funder_id":"https://openalex.org/F4320322698","funder_display_name":"Yunnan University of Finance and Economics"},{"id":"https://openalex.org/G4771114432","display_name":null,"funder_award_id":"09ZB102","funder_id":"https://openalex.org/F4320322970","funder_display_name":"Education Department of Sichuan Province"},{"id":"https://openalex.org/G488551063","display_name":null,"funder_award_id":"09ZB102","funder_id":"https://openalex.org/F4320324731","funder_display_name":"Yunnan University"},{"id":"https://openalex.org/G6103329348","display_name":null,"funder_award_id":"11ZB146","funder_id":"https://openalex.org/F4320324731","funder_display_name":"Yunnan University"}],"funders":[{"id":"https://openalex.org/F4320322698","display_name":"Yunnan University of Finance and Economics","ror":"https://ror.org/04rhev598"},{"id":"https://openalex.org/F4320322970","display_name":"Education Department of Sichuan Province","ror":"https://ror.org/05s1c4z27"},{"id":"https://openalex.org/F4320324731","display_name":"Yunnan University","ror":"https://ror.org/0040axw97"}],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2036053795.pdf","grobid_xml":"https://content.openalex.org/works/W2036053795.grobid-xml"},"referenced_works_count":25,"referenced_works":["https://openalex.org/W93786226","https://openalex.org/W119258514","https://openalex.org/W1487976166","https://openalex.org/W1519983590","https://openalex.org/W1876574230","https://openalex.org/W1964356434","https://openalex.org/W1966410363","https://openalex.org/W1968337487","https://openalex.org/W1969324614","https://openalex.org/W1991765628","https://openalex.org/W1992322822","https://openalex.org/W2008590178","https://openalex.org/W2030275160","https://openalex.org/W2031820100","https://openalex.org/W2032068878","https://openalex.org/W2035973668","https://openalex.org/W2052611235","https://openalex.org/W2055132062","https://openalex.org/W2056891296","https://openalex.org/W2059785880","https://openalex.org/W2067080690","https://openalex.org/W2091759340","https://openalex.org/W2099681657","https://openalex.org/W2134851358","https://openalex.org/W2257123523"],"related_works":["https://openalex.org/W2909053289","https://openalex.org/W2071359864","https://openalex.org/W2107828318","https://openalex.org/W2014530303","https://openalex.org/W2800221421","https://openalex.org/W2153919586","https://openalex.org/W2143945241","https://openalex.org/W2019736576","https://openalex.org/W2136054732","https://openalex.org/W2011239293"],"abstract_inverted_index":{"The":[0,60],"purpose":[1],"of":[2,15,24,26,29,41],"this":[3],"paper":[4,65],"is":[5],"using":[6],"Korpelevich\u2032s":[7],"extragradient":[8],"method":[9],"to":[10],"study":[11],"the":[12,64],"existence":[13,52],"problem":[14,20],"solutions":[16],"and":[17,54,67],"approximation":[18,55],"solvability":[19,56],"for":[21],"a":[22],"class":[23],"systems":[25],"finite":[27],"family":[28],"general":[30],"nonlinear":[31],"variational":[32,42],"inequality":[33,43],"in":[34,63],"Banach":[35],"spaces,":[36],"which":[37],"includes":[38],"many":[39],"kinds":[40],"problems":[44],"as":[45],"special":[46],"cases.":[47],"Under":[48],"suitable":[49],"conditions,":[50],"some":[51,69],"theorems":[53,57],"are":[58],"proved.":[59],"results":[61],"presented":[62],"improve":[66],"extend":[68],"recent":[70],"results.":[71]},"counts_by_year":[{"year":2018,"cited_by_count":1},{"year":2014,"cited_by_count":1}],"updated_date":"2026-07-13T07:31:44.756512","created_date":"2025-10-10T00:00:00"}
