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The sufficiency of Kuhn-Tucker optimality conditions and appropriate duality results are proved involving<mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" id=\"M4\"><mml:mo stretchy=\"false\">(<\/mml:mo><mml:mi>F<\/mml:mi><mml:mo>,<\/mml:mo><mml:mi>\u03c1<\/mml:mi><mml:mo stretchy=\"false\">)<\/mml:mo><\/mml:math>-convex,<mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" id=\"M5\"><mml:mo stretchy=\"false\">(<\/mml:mo><mml:mi>F<\/mml:mi><mml:mo>,<\/mml:mo><mml:mi>\u03b1<\/mml:mi><mml:mo>,<\/mml:mo><mml:mi>\u03c1<\/mml:mi><mml:mo>,<\/mml:mo><mml:mi>d<\/mml:mi><mml:mo stretchy=\"false\">)<\/mml:mo><\/mml:math>-convex, and generalized<mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" id=\"M6\"><mml:mo stretchy=\"false\">(<\/mml:mo><mml:mi>F<\/mml:mi><mml:mo>,<\/mml:mo><mml:mi>\u03b1<\/mml:mi><mml:mo>,<\/mml:mo><mml:mi>\u03c1<\/mml:mi><mml:mo>,<\/mml:mo><mml:mi>d<\/mml:mi><mml:mo stretchy=\"false\">)<\/mml:mo><\/mml:math>-convex functions.<\/jats:p>","DOI":"10.1155\/2013\/708979","type":"journal-article","created":{"date-parts":[[2013,11,27]],"date-time":"2013-11-27T18:02:21Z","timestamp":1385575341000},"page":"1-9","source":"Crossref","is-referenced-by-count":2,"title":["Optimality Conditions and Duality of Three Kinds of Nonlinear Fractional Programming Problems"],"prefix":"10.1155","volume":"2013","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-6345-4235","authenticated-orcid":true,"given":"Xiaomin","family":"Zhang","sequence":"first","affiliation":[{"name":"Department of Mathematics, Chengdu University of Information Technology, Sichuan 610225, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Zezhong","family":"Wu","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Chengdu University of Information Technology, Sichuan 610225, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"311","reference":[{"year":"1944","key":"1"},{"key":"2","doi-asserted-by":"publisher","DOI":"10.1016\/0022-247X(92)90303-U"},{"key":"3","doi-asserted-by":"publisher","DOI":"10.1006\/jmaa.1994.1139"},{"key":"4","doi-asserted-by":"publisher","DOI":"10.1287\/moor.8.2.231"},{"key":"5","doi-asserted-by":"publisher","DOI":"10.1023\/A:1017540412396"},{"key":"6","doi-asserted-by":"publisher","DOI":"10.1023\/A:1026041403408"},{"key":"7","doi-asserted-by":"publisher","DOI":"10.1017\/S000497270000277X"},{"key":"8","doi-asserted-by":"publisher","DOI":"10.1017\/S0004972700010303"},{"key":"9","doi-asserted-by":"publisher","DOI":"10.1017\/S0334270000007372"},{"key":"10","doi-asserted-by":"publisher","DOI":"10.1016\/0022-247X(89)90321-1"},{"year":"2008","key":"11"},{"year":"1992","key":"12"},{"issue":"5","key":"14","first-page":"594","volume":"30","year":"2007","journal-title":"Journal of Sichuan Normal University"},{"year":"1969","key":"15"}],"container-title":["Advances in Operations Research"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/downloads.hindawi.com\/journals\/aor\/2013\/708979.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/downloads.hindawi.com\/journals\/aor\/2013\/708979.xml","content-type":"application\/xml","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/downloads.hindawi.com\/journals\/aor\/2013\/708979.pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2016,7,30]],"date-time":"2016-07-30T14:19:16Z","timestamp":1469888356000},"score":1,"resource":{"primary":{"URL":"http:\/\/www.hindawi.com\/journals\/aor\/2013\/708979\/"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2013]]},"references-count":14,"alternative-id":["708979","708979"],"URL":"https:\/\/doi.org\/10.1155\/2013\/708979","relation":{},"ISSN":["1687-9147","1687-9155"],"issn-type":[{"type":"print","value":"1687-9147"},{"type":"electronic","value":"1687-9155"}],"subject":[],"published":{"date-parts":[[2013]]}}}