{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2024,6,11]],"date-time":"2024-06-11T07:40:18Z","timestamp":1718091618321},"reference-count":28,"publisher":"Wiley","issue":"1","license":[{"start":{"date-parts":[[2012,4,3]],"date-time":"2012-04-03T00:00:00Z","timestamp":1333411200000},"content-version":"vor","delay-in-days":93,"URL":"http:\/\/creativecommons.org\/licenses\/by\/3.0\/"}],"funder":[{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["70972056","71172084","CDJSK11003"],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":["onlinelibrary.wiley.com"],"crossmark-restriction":true},"short-container-title":["Journal of Applied Mathematics"],"published-print":{"date-parts":[[2012,1]]},"abstract":"We consider a generalized \u03b5<\/jats:italic>\u2010vector equilibrium problem which contain vector equilibrium problems and vector variational inequalities as special cases. By using the KKM theorem, we obtain some existence theorems for the generalized \u03b5<\/jats:italic>\u2010vector equilibrium problem. We also investigate the duality of this generalized \u03b5<\/jats:italic>\u2010vector equilibrium problem and discuss the equivalence relation between solutions of primal and dual problems.<\/jats:p>","DOI":"10.1155\/2012\/674512","type":"journal-article","created":{"date-parts":[[2012,4,3]],"date-time":"2012-04-03T21:43:24Z","timestamp":1333489404000},"update-policy":"http:\/\/dx.doi.org\/10.1002\/crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Existence and Duality of Generalized \u03b5<\/i>\u2010Vector Equilibrium Problems"],"prefix":"10.1155","volume":"2012","author":[{"given":"Hong-Yong","family":"Fu","sequence":"first","affiliation":[]},{"given":"Bin","family":"Dan","sequence":"additional","affiliation":[]},{"given":"Xiang-Yu","family":"Liu","sequence":"additional","affiliation":[]}],"member":"311","published-online":{"date-parts":[[2012,4,3]]},"reference":[{"key":"e_1_2_6_1_2","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-4613-0299-5"},{"key":"e_1_2_6_2_2","series-title":"Lecture Notes in Economics and Mathematical Systems","volume-title":"Vector Optimization: Set-Valued and Variational Analysis","author":"Chen G. Y.","year":"2005"},{"key":"e_1_2_6_3_2","doi-asserted-by":"publisher","DOI":"10.1016\/0362-546X(93)90052-T"},{"key":"e_1_2_6_4_2","doi-asserted-by":"publisher","DOI":"10.1016\/0893-9659(95)00099-2"},{"key":"e_1_2_6_5_2","doi-asserted-by":"publisher","DOI":"10.1016\/S0893-9659(98)00050-0"},{"key":"e_1_2_6_6_2","doi-asserted-by":"publisher","DOI":"10.1023\/A:1017581009670"},{"key":"e_1_2_6_7_2","doi-asserted-by":"publisher","DOI":"10.1023\/A:1015366419163"},{"key":"e_1_2_6_8_2","doi-asserted-by":"publisher","DOI":"10.1007\/s10957-007-9342-6"},{"key":"e_1_2_6_9_2","doi-asserted-by":"publisher","DOI":"10.1081\/NFA-100108310"},{"key":"e_1_2_6_10_2","doi-asserted-by":"publisher","DOI":"10.1007\/s11590-009-0141-x"},{"key":"e_1_2_6_11_2","unstructured":"SunX. K.andLiS. J. Duality and Farkas-type results for extended Ky Fan inequalities with DC functions submitted toOptimization Lettershttps:\/\/doi.org\/10.1007\/s11590%2D011%2D0434%2D8."},{"key":"e_1_2_6_12_2","doi-asserted-by":"publisher","DOI":"10.1137\/S0363012995292561"},{"key":"e_1_2_6_13_2","doi-asserted-by":"publisher","DOI":"10.1016\/S0898-1221(99)00105-4"},{"key":"e_1_2_6_14_2","doi-asserted-by":"publisher","DOI":"10.1080\/02331930290019440"},{"key":"e_1_2_6_15_2","doi-asserted-by":"publisher","DOI":"10.1016\/S0377-2217(03)00206-6"},{"key":"e_1_2_6_16_2","first-page":"1787","article-title":"On \u03b5-optimality conditions for convex set-valued optimization problems","volume":"13","author":"Lee G. M.","year":"2009","journal-title":"Taiwanese Journal of Mathematics"},{"key":"e_1_2_6_17_2","doi-asserted-by":"publisher","DOI":"10.1080\/02331939608844170"},{"key":"e_1_2_6_18_2","doi-asserted-by":"publisher","DOI":"10.1007\/s10957-008-9403-5"},{"key":"e_1_2_6_19_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.jmaa.2009.02.041"},{"key":"e_1_2_6_20_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.na.2010.01.031"},{"key":"e_1_2_6_21_2","doi-asserted-by":"publisher","DOI":"10.1007\/s10898-010-9641-6"},{"key":"e_1_2_6_22_2","doi-asserted-by":"crossref","unstructured":"SunX. K.andLiS. J. Duality and gap function for generalized multivalued\u03b5-vector variational inequality submitted toApplicable Analysishttps:\/\/doi.org\/10.1080\/00036811.2011.628940.","DOI":"10.1080\/00036811.2011.628940"},{"key":"e_1_2_6_23_2","volume-title":"Vector Optimization-Theory, Applications and Extensions","author":"Jahn J.","year":"2004"},{"key":"e_1_2_6_24_2","doi-asserted-by":"publisher","DOI":"10.1080\/01630560802099274"},{"key":"e_1_2_6_25_2","series-title":"Mathematics in Science and Engineering","volume-title":"Theory of Multiobjective Optimization","author":"Sawaragi Y.","year":"1985"},{"key":"e_1_2_6_26_2","unstructured":"LiS. J.andGuoX. L. Calculus rules of generalized\u03b5-subdifferentialfor vector valued mappings and applications Journal of Industrial and Management Optimization. In press."},{"key":"e_1_2_6_27_2","doi-asserted-by":"publisher","DOI":"10.1007\/BF01353421"},{"key":"e_1_2_6_28_2","doi-asserted-by":"publisher","DOI":"10.1007\/BF01415945"}],"container-title":["Journal of Applied Mathematics"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/downloads.hindawi.com\/journals\/jam\/2012\/674512.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/downloads.hindawi.com\/journals\/jam\/2012\/674512.xml","content-type":"application\/xml","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/pdf\/10.1155\/2012\/674512","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2024,6,11]],"date-time":"2024-06-11T07:09:51Z","timestamp":1718089791000},"score":1,"resource":{"primary":{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/10.1155\/2012\/674512"}},"subtitle":[],"editor":[{"given":"Said","family":"Abbasbandy","sequence":"additional","affiliation":[]}],"short-title":[],"issued":{"date-parts":[[2012,1]]},"references-count":28,"journal-issue":{"issue":"1","published-print":{"date-parts":[[2012,1]]}},"alternative-id":["10.1155\/2012\/674512"],"URL":"http:\/\/dx.doi.org\/10.1155\/2012\/674512","archive":["Portico"],"relation":{},"ISSN":["1110-757X","1687-0042"],"issn-type":[{"value":"1110-757X","type":"print"},{"value":"1687-0042","type":"electronic"}],"subject":[],"published":{"date-parts":[[2012,1]]},"assertion":[{"value":"2011-11-15","order":0,"name":"received","label":"Received","group":{"name":"publication_history","label":"Publication History"}},{"value":"2012-02-02","order":1,"name":"accepted","label":"Accepted","group":{"name":"publication_history","label":"Publication History"}},{"value":"2012-04-03","order":2,"name":"published","label":"Published","group":{"name":"publication_history","label":"Publication History"}}]}}
