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Using the KKM technique, we obtain the existence of solutions for the generalized mixed equilibrium\nproblem in Banach spaces. Furthermore, we also introduce a hybrid projection algorithm for finding a common element\nin the solution set of a generalized mixed equilibrium problem and the fixed point set of an asymptotically nonexpansive\nmapping. The strong convergence theorem of the proposed sequence is obtained in a Banach space setting. The main\nresults extend various results existing in the current literature.<\/jats:p>","DOI":"10.1155\/2012\/790592","type":"journal-article","created":{"date-parts":[[2012,4,10]],"date-time":"2012-04-10T21:03:11Z","timestamp":1334091791000},"update-policy":"https:\/\/doi.org\/10.1002\/crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["New Generalized Mixed Equilibrium Problem with Respect to Relaxed Semi\u2010Monotone Mappings in Banach Spaces"],"prefix":"10.1155","volume":"2012","author":[{"given":"Rabian","family":"Wangkeeree","sequence":"first","affiliation":[]},{"given":"Pakkapon","family":"Preechasilp","sequence":"additional","affiliation":[]}],"member":"311","published-online":{"date-parts":[[2012,4,10]]},"reference":[{"key":"e_1_2_6_1_2","doi-asserted-by":"publisher","DOI":"10.1023\/A:1025499305742"},{"key":"e_1_2_6_2_2","doi-asserted-by":"publisher","DOI":"10.1006\/jmaa.1998.6245"},{"key":"e_1_2_6_3_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.cam.2007.02.022"},{"key":"e_1_2_6_4_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.camwa.2011.03.029"},{"key":"e_1_2_6_5_2","unstructured":"YaoY. yaoyonghong@yahoo.cn LiouY.-C. andsimplex_liou@hotmail.com KangS. 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