{"id":"https://openalex.org/W4283396047","doi":"https://doi.org/10.3390/sym14040760","title":"The Convergence Results of Differential Variational Inequality Problems","display_name":"The Convergence Results of Differential Variational Inequality Problems","publication_year":2022,"publication_date":"2022-04-06","ids":{"openalex":"https://openalex.org/W4283396047","doi":"https://doi.org/10.3390/sym14040760"},"language":"en","primary_location":{"id":"doi:10.3390/sym14040760","is_oa":true,"landing_page_url":"https://doi.org/10.3390/sym14040760","pdf_url":"https://www.mdpi.com/2073-8994/14/4/760/pdf?version=1649252732","source":{"id":"https://openalex.org/S190787756","display_name":"Symmetry","issn_l":"2073-8994","issn":["2073-8994"],"is_oa":true,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Symmetry","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","doaj"],"open_access":{"is_oa":true,"oa_status":"gold","oa_url":"https://www.mdpi.com/2073-8994/14/4/760/pdf?version=1649252732","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5102157579","display_name":"Shih-sen Chang","orcid":null},"institutions":[{"id":"https://openalex.org/I184693016","display_name":"China Medical University","ror":"https://ror.org/00v408z34","country_code":"TW","type":"education","lineage":["https://openalex.org/I184693016"]}],"countries":["TW"],"is_corresponding":true,"raw_author_name":"Shih-Sen Chang","raw_affiliation_strings":["Center for General Education, China Medical University, Taichung 40402, Taiwan"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Center for General Education, China Medical University, Taichung 40402, Taiwan","institution_ids":["https://openalex.org/I184693016"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5035737050","display_name":"Salahuddin Salahuddin","orcid":null},"institutions":[{"id":"https://openalex.org/I91450128","display_name":"Jazan University","ror":"https://ror.org/02bjnq803","country_code":"SA","type":"education","lineage":["https://openalex.org/I91450128"]}],"countries":["SA"],"is_corresponding":false,"raw_author_name":"Salahuddin","raw_affiliation_strings":["Department of Mathematics, Jazan University, Jazan 45142, Saudi Arabia"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Jazan University, Jazan 45142, Saudi Arabia","institution_ids":["https://openalex.org/I91450128"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5054621625","display_name":"Lin Wang","orcid":"https://orcid.org/0000-0001-8137-2401"},"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":"Lin Wang","raw_affiliation_strings":["College of Statistics and Mathematics, Yunnan University of Finance and Economics, Kunming 650221, China"],"raw_orcid":"https://orcid.org/0000-0001-8137-2401","affiliations":[{"raw_affiliation_string":"College of Statistics and Mathematics, Yunnan University of Finance and Economics, Kunming 650221, China","institution_ids":["https://openalex.org/I49185572"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5088976305","display_name":"Zhaoli Ma","orcid":"https://orcid.org/0000-0002-7347-6929"},"institutions":[{"id":"https://openalex.org/I4210160657","display_name":"Yunnan Open University","ror":"https://ror.org/04egk7864","country_code":"CN","type":"education","lineage":["https://openalex.org/I4210160657"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Zhaoli Ma","raw_affiliation_strings":["College of Public Foundation, Yunnan Open University, Kunming 650221, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"College of Public Foundation, Yunnan Open University, Kunming 650221, China","institution_ids":["https://openalex.org/I4210160657"]}]}],"institutions":[],"countries_distinct_count":3,"institutions_distinct_count":4,"corresponding_author_ids":["https://openalex.org/A5102157579"],"corresponding_institution_ids":["https://openalex.org/I184693016"],"apc_list":{"value":2000,"currency":"CHF","value_usd":2165},"apc_paid":{"value":2000,"currency":"CHF","value_usd":2165},"fwci":0.6089,"has_fulltext":false,"cited_by_count":4,"citation_normalized_percentile":{"value":0.70176335,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":96},"biblio":{"volume":"14","issue":"4","first_page":"760","last_page":"760"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12809","display_name":"Contact Mechanics and Variational Inequalities","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/T12809","display_name":"Contact Mechanics and Variational Inequalities","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/T10545","display_name":"Optimization and Variational Analysis","score":0.9898999929428101,"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/T11115","display_name":"Topology Optimization in Engineering","score":0.9890000224113464,"subfield":{"id":"https://openalex.org/subfields/2205","display_name":"Civil and Structural Engineering"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.8091830611228943},{"id":"https://openalex.org/keywords/variational-inequality","display_name":"Variational inequality","score":0.7255008816719055},{"id":"https://openalex.org/keywords/lipschitz-continuity","display_name":"Lipschitz continuity","score":0.642332136631012},{"id":"https://openalex.org/keywords/sequence","display_name":"Sequence (biology)","score":0.6270555257797241},{"id":"https://openalex.org/keywords/banach-space","display_name":"Banach space","score":0.6269496083259583},{"id":"https://openalex.org/keywords/convergence","display_name":"Convergence (economics)","score":0.5851020812988281},{"id":"https://openalex.org/keywords/compact-space","display_name":"Compact space","score":0.5668436288833618},{"id":"https://openalex.org/keywords/monotonic-function","display_name":"Monotonic function","score":0.5313803553581238},{"id":"https://openalex.org/keywords/limit-of-a-sequence","display_name":"Limit of a sequence","score":0.46316561102867126},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.4467056691646576},{"id":"https://openalex.org/keywords/differential","display_name":"Differential (mechanical device)","score":0.4146210551261902},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.36695387959480286},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.34964117407798767},{"id":"https://openalex.org/keywords/limit","display_name":"Limit (mathematics)","score":0.150719553232193}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8091830611228943},{"id":"https://openalex.org/C161999928","wikidata":"https://www.wikidata.org/wiki/Q4556320","display_name":"Variational inequality","level":2,"score":0.7255008816719055},{"id":"https://openalex.org/C22324862","wikidata":"https://www.wikidata.org/wiki/Q652707","display_name":"Lipschitz continuity","level":2,"score":0.642332136631012},{"id":"https://openalex.org/C2778112365","wikidata":"https://www.wikidata.org/wiki/Q3511065","display_name":"Sequence (biology)","level":2,"score":0.6270555257797241},{"id":"https://openalex.org/C132954091","wikidata":"https://www.wikidata.org/wiki/Q194397","display_name":"Banach space","level":2,"score":0.6269496083259583},{"id":"https://openalex.org/C2777303404","wikidata":"https://www.wikidata.org/wiki/Q759757","display_name":"Convergence (economics)","level":2,"score":0.5851020812988281},{"id":"https://openalex.org/C18648836","wikidata":"https://www.wikidata.org/wiki/Q381892","display_name":"Compact space","level":2,"score":0.5668436288833618},{"id":"https://openalex.org/C72169020","wikidata":"https://www.wikidata.org/wiki/Q194404","display_name":"Monotonic function","level":2,"score":0.5313803553581238},{"id":"https://openalex.org/C71287196","wikidata":"https://www.wikidata.org/wiki/Q847204","display_name":"Limit of a sequence","level":3,"score":0.46316561102867126},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.4467056691646576},{"id":"https://openalex.org/C93226319","wikidata":"https://www.wikidata.org/wiki/Q193137","display_name":"Differential (mechanical device)","level":2,"score":0.4146210551261902},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.36695387959480286},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.34964117407798767},{"id":"https://openalex.org/C151201525","wikidata":"https://www.wikidata.org/wiki/Q177239","display_name":"Limit (mathematics)","level":2,"score":0.150719553232193},{"id":"https://openalex.org/C50522688","wikidata":"https://www.wikidata.org/wiki/Q189833","display_name":"Economic growth","level":1,"score":0.0},{"id":"https://openalex.org/C146978453","wikidata":"https://www.wikidata.org/wiki/Q3798668","display_name":"Aerospace engineering","level":1,"score":0.0},{"id":"https://openalex.org/C127413603","wikidata":"https://www.wikidata.org/wiki/Q11023","display_name":"Engineering","level":0,"score":0.0},{"id":"https://openalex.org/C54355233","wikidata":"https://www.wikidata.org/wiki/Q7162","display_name":"Genetics","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/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.3390/sym14040760","is_oa":true,"landing_page_url":"https://doi.org/10.3390/sym14040760","pdf_url":"https://www.mdpi.com/2073-8994/14/4/760/pdf?version=1649252732","source":{"id":"https://openalex.org/S190787756","display_name":"Symmetry","issn_l":"2073-8994","issn":["2073-8994"],"is_oa":true,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Symmetry","raw_type":"journal-article"},{"id":"pmh:oai:doaj.org/article:59d21f9491e5449595a6efe717d5eae2","is_oa":true,"landing_page_url":"https://doaj.org/article/59d21f9491e5449595a6efe717d5eae2","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":"Symmetry, Vol 14, Iss 4, p 760 (2022)","raw_type":"article"},{"id":"pmh:oai:mdpi.com:/2073-8994/14/4/760/","is_oa":true,"landing_page_url":"https://dx.doi.org/10.3390/sym14040760","pdf_url":null,"source":{"id":"https://openalex.org/S4306400947","display_name":"MDPI (MDPI AG)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I4210097602","host_organization_name":"Multidisciplinary Digital Publishing Institute (Switzerland)","host_organization_lineage":["https://openalex.org/I4210097602"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Symmetry","raw_type":"Text"}],"best_oa_location":{"id":"doi:10.3390/sym14040760","is_oa":true,"landing_page_url":"https://doi.org/10.3390/sym14040760","pdf_url":"https://www.mdpi.com/2073-8994/14/4/760/pdf?version=1649252732","source":{"id":"https://openalex.org/S190787756","display_name":"Symmetry","issn_l":"2073-8994","issn":["2073-8994"],"is_oa":true,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Symmetry","raw_type":"journal-article"},"sustainable_development_goals":[{"score":0.7099999785423279,"display_name":"Reduced inequalities","id":"https://metadata.un.org/sdg/10"}],"awards":[],"funders":[],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W4283396047.pdf","grobid_xml":"https://content.openalex.org/works/W4283396047.grobid-xml"},"referenced_works_count":27,"referenced_works":["https://openalex.org/W1516681311","https://openalex.org/W1527296550","https://openalex.org/W2074452547","https://openalex.org/W2078742969","https://openalex.org/W2096143754","https://openalex.org/W2109783572","https://openalex.org/W2260520465","https://openalex.org/W2328285789","https://openalex.org/W2484453099","https://openalex.org/W2490228683","https://openalex.org/W2562910626","https://openalex.org/W2566578539","https://openalex.org/W2616991700","https://openalex.org/W2777926324","https://openalex.org/W2783352638","https://openalex.org/W2803718315","https://openalex.org/W2909818800","https://openalex.org/W2912151246","https://openalex.org/W2942272966","https://openalex.org/W2966204037","https://openalex.org/W2967505371","https://openalex.org/W2985272081","https://openalex.org/W3014013933","https://openalex.org/W3203210294","https://openalex.org/W4205449078","https://openalex.org/W6747162076","https://openalex.org/W6766958552"],"related_works":["https://openalex.org/W2487640660","https://openalex.org/W2612526717","https://openalex.org/W2121543990","https://openalex.org/W2402800040","https://openalex.org/W175486093","https://openalex.org/W3118444755","https://openalex.org/W4221091651","https://openalex.org/W2259276142","https://openalex.org/W1980756862","https://openalex.org/W4237486913"],"abstract_inverted_index":{"In":[0],"this":[1],"work,":[2],"we":[3,69],"suggest":[4],"a":[5,15,18,23,33],"differential":[6,77],"variational":[7,78],"inequality":[8,79],"in":[9],"reflexive":[10],"Banach":[11],"spaces":[12],"and":[13,22,39,65],"construct":[14],"sequence":[16],"with":[17],"set":[19],"of":[20,47],"constraints":[21],"penalty":[24,29],"parameter.":[25],"We":[26],"use":[27],"the":[28,37,45,48,71,76],"method":[30],"to":[31,36,43],"prove":[32,44],"unique":[34],"solution":[35],"problem":[38,74,80],"make":[40],"suitable":[41],"assumptions":[42],"convergence":[46],"sequence.":[49],"The":[50],"proof":[51],"is":[52],"based":[53],"on":[54],"arguments":[55],"for":[56,75],"compactness,":[57],"symmetry,":[58],"pseudomonotonicity,":[59],"Mosco":[60],"convergence,":[61],"inverse":[62],"strong":[63],"monotonicity":[64],"Lipschitz":[66],"continuity.":[67],"Finally,":[68],"discuss":[70],"boundary":[72],"value":[73],"as":[81],"an":[82],"application.":[83]},"counts_by_year":[{"year":2024,"cited_by_count":2},{"year":2023,"cited_by_count":1},{"year":2022,"cited_by_count":1}],"updated_date":"2026-05-21T09:19:25.381259","created_date":"2025-10-10T00:00:00"}