{"id":"https://openalex.org/W606402000","doi":"https://doi.org/10.1007/978-1-4613-0299-5","title":"Vector Variational Inequalities and Vector Equilibria: Mathematical Theories","display_name":"Vector Variational Inequalities and Vector Equilibria: Mathematical Theories","publication_year":2011,"publication_date":"2011-09-17","ids":{"openalex":"https://openalex.org/W606402000","doi":"https://doi.org/10.1007/978-1-4613-0299-5","mag":"606402000"},"language":"en","primary_location":{"id":"pmh:oai:aleph.bib-bvb.de:BVB01-017467729","doi":null,"is_oa":false,"landing_page_url":"http://bvbr.bib-bvb.de:8991/F?func=service&amp;doc_library=BVB01&amp;local_base=BVB01&amp;doc_number=017467729&amp;sequence=000001&amp;line_number=0001&amp;func_code=DB_RECORDS&amp;service_type=MEDIA","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"text"},"volume":null,"type":"article","indexed_in":[],"open_access":{"is_oa":false,"oa_status":"closed","oa_url":null,"any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5108374423","display_name":"F. Giannessi","orcid":null,"observed_orcids":[]},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"F. Giannessi","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"corresponding_author_ids":["https://openalex.org/A5108374423"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":21.5278,"has_fulltext":false,"cited_by_count":234,"citation_normalized_percentile":{"value":0.99755419,"is_in_top_1_percent":true,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":89,"max":100},"biblio":{"volume":null,"issue":null,"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":0.9994999766349792,"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":0.9994999766349792,"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":9.999999747378752e-05,"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/T11564","display_name":"Mathematical Inequalities and Applications","score":0.0,"subfield":{"id":"https://openalex.org/subfields/2604","display_name":"Applied Mathematics"},"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/vector-variational-inequalities","display_name":"vector variational inequalities","score":0.9229999780654907},{"id":"https://openalex.org/keywords/vector-equilibrium-problems","display_name":"vector equilibrium problems","score":0.996999979019165},{"id":"https://openalex.org/keywords/existence-of-solutions","display_name":"existence of solutions","score":0.722000002861023},{"id":"https://openalex.org/keywords/gap-function","display_name":"gap function","score":0.8199999928474426},{"id":"https://openalex.org/keywords/traffic-equilibrium","display_name":"traffic equilibrium","score":0.6240000128746033},{"id":"https://openalex.org/keywords/image-space-analysis","display_name":"image space analysis","score":0.8790000081062317},{"id":"https://openalex.org/keywords/scalarization","display_name":"scalarization","score":0.6890000104904175},{"id":"https://openalex.org/keywords/super-efficiency","display_name":"super efficiency","score":0.9120000004768372},{"id":"https://openalex.org/keywords/saddle-point-problems","display_name":"saddle point problems","score":0.8830000162124634},{"id":"https://openalex.org/keywords/ekeland-s-variational-principle","display_name":"Ekeland's variational principle","score":0.9539999961853027},{"id":"https://openalex.org/keywords/minty-variational-inequality","display_name":"Minty variational inequality","score":0.8029999732971191},{"id":"https://openalex.org/keywords/multi-objective-optimization","display_name":"multi-objective optimization","score":0.5830000042915344}],"concepts":[{"id":"https://openalex.org/C161999928","wikidata":"https://www.wikidata.org/wiki/Q4556320","display_name":"Variational inequality","level":2,"score":0.8013418912887573},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7234541177749634},{"id":"https://openalex.org/C171739935","wikidata":"https://www.wikidata.org/wiki/Q726210","display_name":"Normed vector space","level":2,"score":0.6064388155937195},{"id":"https://openalex.org/C164088818","wikidata":"https://www.wikidata.org/wiki/Q7917833","display_name":"Vector optimization","level":4,"score":0.5757371187210083},{"id":"https://openalex.org/C45633534","wikidata":"https://www.wikidata.org/wiki/Q752487","display_name":"Dual space","level":2,"score":0.4803970158100128},{"id":"https://openalex.org/C147663694","wikidata":"https://www.wikidata.org/wiki/Q1144631","display_name":"Curl (programming language)","level":2,"score":0.45973268151283264},{"id":"https://openalex.org/C13336665","wikidata":"https://www.wikidata.org/wiki/Q125977","display_name":"Vector space","level":2,"score":0.4271278977394104},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.4218613803386688},{"id":"https://openalex.org/C523394659","wikidata":"https://www.wikidata.org/wiki/Q17086892","display_name":"Variational analysis","level":2,"score":0.412860244512558},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.4038889408111572},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.3479729890823364},{"id":"https://openalex.org/C137836250","wikidata":"https://www.wikidata.org/wiki/Q984063","display_name":"Optimization problem","level":2,"score":0.2000027596950531},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.19319361448287964},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.09587883949279785},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.0},{"id":"https://openalex.org/C122357587","wikidata":"https://www.wikidata.org/wiki/Q6934508","display_name":"Multi-swarm optimization","level":3,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"pmh:oai:aleph.bib-bvb.de:BVB01-017467729","doi":null,"is_oa":false,"landing_page_url":"http://bvbr.bib-bvb.de:8991/F?func=service&amp;doc_library=BVB01&amp;local_base=BVB01&amp;doc_number=017467729&amp;sequence=000001&amp;line_number=0001&amp;func_code=DB_RECORDS&amp;service_type=MEDIA","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"text"},{"id":"pmh:oai:cds.cern.ch:2023723","doi":"https://doi.org/10.1007/978-1-4613-0299-5","is_oa":false,"landing_page_url":"http://cds.cern.ch/record/2023723","pdf_url":null,"source":{"id":"https://openalex.org/S4306402195","display_name":"CERN Document Server (European Organization for Nuclear Research)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I67311998","host_organization_name":"European Organization for Nuclear Research","host_organization_lineage":["https://openalex.org/I67311998"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":null},{"id":"mag:606402000","doi":null,"is_oa":false,"landing_page_url":"https://babordplus.u-bordeaux.fr/notice.php?q=id:2741028","pdf_url":null,"source":null,"license":null,"license_id":null,"version":null,"is_accepted":false,"is_published":null,"raw_source_name":null,"raw_type":null}],"best_oa_location":null,"sustainable_development_goals":[],"sustainable_development_goals_aurora":[{"score":0.4399999976158142,"id":"https://metadata.un.org/sdg/10","display_name":"Reduced inequalities"}],"study_designs":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":0,"referenced_works":[],"related_works":["https://openalex.org/W2481311888","https://openalex.org/W154593720","https://openalex.org/W1484024929","https://openalex.org/W1599607462","https://openalex.org/W596285643","https://openalex.org/W2088855121","https://openalex.org/W2022706580","https://openalex.org/W19033009","https://openalex.org/W113278869","https://openalex.org/W2087625147","https://openalex.org/W2079936218","https://openalex.org/W2027475013","https://openalex.org/W1986517159","https://openalex.org/W1537058183","https://openalex.org/W2022888931","https://openalex.org/W2056899550","https://openalex.org/W1979188159","https://openalex.org/W2054663037","https://openalex.org/W1996810073","https://openalex.org/W19249476"],"abstract_inverted_index":{"Preface.":[0],"Vector":[1,5,11,26,37,48,61,64,80,90,102,118,135,146,152,177,182,190,197,204,210,226,234,240,246,250,256,261,274,281,288,291,295,306,323,330,335,344],"Equilibrium":[2,73,147,262,292],"Problems":[3,179,192,263,325,337],"and":[4,14,67,109,120,126,222,249,294,303,314,333],"Variational":[6,38,49,65,121,136,167,183,198,212,235,251,257,275,282,289,307,331,345],"Inequalities":[7,13,28,39,50,66,82,92,168,199,242,252,258,276,283,308],"A.H.":[8,17],"Ansari.":[9],"Generalized":[10,25,79,89,239,255],"Variational-Like":[12,27,81,91,103,241],"their":[15],"Scalarization":[16,132],"Ansari,":[18],"et":[19,31,42,130,156,195,216],"al.":[20,32,43,131,157,196,217],"Existence":[21,44,57,159,173],"of":[22,45,58,69,117,160,164,174,219,273,316],"Solutions":[23,46,59,165,175,221],"for":[24,36,47,105,134,144,166,176,188],"S.-S.":[29],"Chang,":[30],"On":[33,55,114,232,245,269,279,301],"Gap":[34],"Functions":[35],"G.-Y.":[40,51,286],"Chen,":[41,52],"S.-H.":[53],"Hou.":[54],"the":[56,115,317],"to":[60],"Complementarity":[62,247,336],"Problems.":[63],"Modelling":[68],"a":[70,145,186,201],"Continuum":[71],"Traffic":[72],"Problem":[74],"P.":[75,228],"Daniele,":[76],"A.":[77],"Maugeri.":[78],"without":[83],"Monotonicity":[84],"X.P.":[85,97],"Ding,":[86,98],"E.":[87,99],"Tarafdar.":[88,100],"with":[93,264],"Cx-eta-Pseudomonotone":[94],"Set-Valued":[95,265],"Mappings":[96,266],"A":[101],"Inequality":[104,137,184,236,332],"Compact":[106],"Acyclic":[107],"Multifunctions":[108],"its":[110],"Applications":[111],"J.":[112,230],"Fu.":[113],"Theory":[116],"Optimization":[119,191,227,296,324],"Inequalities.":[122,346],"Image":[123],"Space":[124,205],"Analysis":[125],"Separation":[127],"F.":[128],"Giannessi,":[129],"Methods":[133],"C.J.":[138],"Goh,":[139],"X.Q.":[140,277,284,297],"Yang.":[141,278],"Super":[142],"Efficiency":[143],"in":[148,200,224,320],"Locally":[149],"Convex":[150],"Topological":[151,203],"Spaces":[153],"X.H.":[154],"Gong,":[155],"The":[158],"Essentially":[161],"Connected":[162],"Components":[163],"G.":[169,237],"Isac,":[170],"G.X.Z.":[171],"Yuan.":[172],"Saddle-Point":[178],"K.R.":[180],"Kazmi.":[181],"as":[185],"Tool":[187],"Studying":[189],"G.M.":[193,206,311],"Lee,":[194,207],"Hausdorff":[202],"S.":[208],"Kum.":[209],"Ekeland":[211],"Principle":[213],"S.J.":[214],"Li,":[215],"Convergence":[218],"Approximate":[220],"Values":[223],"Parametric":[225],"Loridan,":[229],"Morgan.":[231],"Minty":[233],"Mastroeni.":[238],"L.":[243],"Qun.":[244],"Systems":[248],"T.":[253],"Rapcsak.":[254],"W.":[259,267],"Song.":[260,268],"Some":[270],"Equivalent":[271],"Conditions":[272],"Inverse":[280],"Yang,":[285,298],"Chen.":[287],"Inequalities,":[290],"Flow":[293],"C.-J.":[299],"Goh.":[300],"Monotone":[302,305],"Strongly":[304],"N.D.":[309,326],"Yen,":[310,327],"Lee.":[312],"Connectedness":[313],"Stability":[315],"Solution":[318],"Sets":[319],"Linear":[321],"Fractional":[322],"T.D.":[328],"Phuong.":[329],"Implicit":[334],"H.":[338],"Yin,":[339],"C.":[340],"Xu.":[341],"References":[342],"on":[343],"Subject":[347],"Index.":[348],"Contributors.":[349]},"counts_by_year":[{"year":2024,"cited_by_count":1},{"year":2023,"cited_by_count":3},{"year":2021,"cited_by_count":4},{"year":2020,"cited_by_count":10},{"year":2019,"cited_by_count":12},{"year":2018,"cited_by_count":11},{"year":2017,"cited_by_count":12},{"year":2016,"cited_by_count":10},{"year":2015,"cited_by_count":9},{"year":2014,"cited_by_count":19},{"year":2013,"cited_by_count":16},{"year":2012,"cited_by_count":18}],"updated_date":"2026-10-12T09:40:04.860316","created_date":"2025-10-10T00:00:00"}
