{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,7,30]],"date-time":"2025-07-30T13:54:01Z","timestamp":1753883641434,"version":"3.41.2"},"reference-count":26,"publisher":"Wiley","issue":"1","license":[{"start":{"date-parts":[[2012,7,5]],"date-time":"2012-07-05T00:00:00Z","timestamp":1341446400000},"content-version":"vor","delay-in-days":186,"URL":"http:\/\/creativecommons.org\/licenses\/by\/3.0\/"}],"funder":[{"DOI":"10.13039\/100009950","name":"Ministry of Education, Thailand","doi-asserted-by":"crossref","id":[{"id":"10.13039\/100009950","id-type":"DOI","asserted-by":"crossref"}]},{"name":"Office of the Higher Education Commission, Thailand"}],"content-domain":{"domain":["onlinelibrary.wiley.com"],"crossmark-restriction":true},"short-container-title":["Journal of Applied Mathematics"],"published-print":{"date-parts":[[2012,1]]},"abstract":"<jats:p>We first prove the existence of solutions for a generalized mixed equilibrium problem under the new conditions imposed on the given bifunction and introduce the algorithm for solving a common element in the solution set of a generalized mixed equilibrium problem and the common fixed point set of finite family of asymptotically nonexpansive mappings. Next, the strong convergence theorems are obtained, under some appropriate conditions, in uniformly convex and smooth Banach spaces. The main results extend various results existing in the current literature.<\/jats:p>","DOI":"10.1155\/2012\/859492","type":"journal-article","created":{"date-parts":[[2012,7,5]],"date-time":"2012-07-05T06:17:00Z","timestamp":1341469020000},"update-policy":"https:\/\/doi.org\/10.1002\/crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Existence and Strong Convergence Theorems for Generalized Mixed Equilibrium Problems of a Finite Family of Asymptotically Nonexpansive Mappings in Banach Spaces"],"prefix":"10.1155","volume":"2012","author":[{"given":"Rabian","family":"Wangkeeree","sequence":"first","affiliation":[]},{"given":"Hossein","family":"Dehghan","sequence":"additional","affiliation":[]},{"given":"Pakkapon","family":"Preechasilp","sequence":"additional","affiliation":[]}],"member":"311","published-online":{"date-parts":[[2012,7,5]]},"reference":[{"key":"e_1_2_7_1_2","doi-asserted-by":"publisher","DOI":"10.1090\/S0002-9939-1972-0298500-3"},{"volume-title":"Fixed Point Theory for Lipschitzian-Type Mappings with Applications","year":"2000","author":"Agarwal R. P.","key":"e_1_2_7_2_2"},{"key":"e_1_2_7_3_2","doi-asserted-by":"publisher","DOI":"10.1023\/A:1025499305742"},{"key":"e_1_2_7_4_2","first-page":"1","article-title":"Eigenvalue and dynamic problems for variational and hemivariational inequalities","volume":"3","author":"Goeleven D.","year":"1996","journal-title":"Communications on Applied Nonlinear Analysis"},{"key":"e_1_2_7_5_2","first-page":"969","article-title":"On nonlinear variational inequalities","volume":"25","author":"Siddiqi A. H.","year":"1994","journal-title":"Indian Journal of Pure and Applied Mathematics"},{"key":"e_1_2_7_6_2","doi-asserted-by":"publisher","DOI":"10.1016\/S0893-9659(97)00054-2"},{"key":"e_1_2_7_7_2","unstructured":"KamraksaU.andWangkeereeR. Existence theorems and iterative approximation methods for generalized mixed equilibrium problems for a countable family of nonexpansivemappings Journal of Global Optimization. In presshttps:\/\/doi.org\/10.1007\/s10898%2D011%2D9739%2D5."},{"key":"e_1_2_7_8_2","doi-asserted-by":"publisher","DOI":"10.4064\/fm-14-1-132-137"},{"key":"e_1_2_7_9_2","first-page":"123","article-title":"From optimization and variational inequalities to equilibrium problems","volume":"63","author":"Blum E.","year":"1994","journal-title":"The Mathematics Student"},{"key":"e_1_2_7_10_2","first-page":"117","article-title":"Equilibrium programming in Hilbert spaces","volume":"6","author":"Combettes P. L.","year":"2005","journal-title":"Journal of Nonlinear and Convex Analysis"},{"key":"e_1_2_7_11_2","first-page":"1","article-title":"Second-order differential proximal methods for equilibrium problems","volume":"4","author":"Moudafi A.","year":"2003","journal-title":"Journal of Inequalities in Pure and Applied Mathematics"},{"key":"e_1_2_7_12_2","doi-asserted-by":"publisher","DOI":"10.1090\/S0002-9939-1953-0054846-3"},{"key":"e_1_2_7_13_2","doi-asserted-by":"publisher","DOI":"10.1007\/s10957-007-9187-z"},{"key":"e_1_2_7_14_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.amc.2007.06.006"},{"key":"e_1_2_7_15_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.jmaa.2007.09.062"},{"key":"e_1_2_7_16_2","doi-asserted-by":"publisher","DOI":"10.1007\/s10957-007-9187-z"},{"key":"e_1_2_7_17_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.na.2008.02.042"},{"key":"e_1_2_7_18_2","doi-asserted-by":"publisher","DOI":"10.1016\/S0022-247X(02)00458-4"},{"key":"e_1_2_7_19_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.na.2003.10.010"},{"key":"e_1_2_7_20_2","doi-asserted-by":"publisher","DOI":"10.1007\/BF02757276"},{"key":"e_1_2_7_21_2","doi-asserted-by":"publisher","DOI":"10.1016\/0022-247X(79)90024-6"},{"key":"e_1_2_7_22_2","doi-asserted-by":"publisher","DOI":"10.1017\/S0004972700047535"},{"key":"e_1_2_7_23_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.aml.2011.03.051"},{"key":"e_1_2_7_24_2","doi-asserted-by":"publisher","DOI":"10.1155\/2010\/732872"},{"key":"e_1_2_7_25_2","doi-asserted-by":"crossref","DOI":"10.1007\/978-1-4612-4838-5","volume-title":"Nonlinear Functional Analysis and Its Applications\u2014Vol I: Fixed-Point Theorems","author":"Zeidler E.","year":"1986"},{"key":"e_1_2_7_26_2","doi-asserted-by":"publisher","DOI":"10.1016\/S0898-1221(04)90058-2"}],"container-title":["Journal of Applied Mathematics"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/downloads.hindawi.com\/journals\/jam\/2012\/859492.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/downloads.hindawi.com\/journals\/jam\/2012\/859492.xml","content-type":"application\/xml","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/pdf\/10.1155\/2012\/859492","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2024,6,11]],"date-time":"2024-06-11T07:11:53Z","timestamp":1718089913000},"score":1,"resource":{"primary":{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/10.1155\/2012\/859492"}},"subtitle":[],"editor":[{"given":"Giuseppe","family":"Marino","sequence":"additional","affiliation":[]}],"short-title":[],"issued":{"date-parts":[[2012,1]]},"references-count":26,"journal-issue":{"issue":"1","published-print":{"date-parts":[[2012,1]]}},"alternative-id":["10.1155\/2012\/859492"],"URL":"https:\/\/doi.org\/10.1155\/2012\/859492","archive":["Portico"],"relation":{},"ISSN":["1110-757X","1687-0042"],"issn-type":[{"type":"print","value":"1110-757X"},{"type":"electronic","value":"1687-0042"}],"subject":[],"published":{"date-parts":[[2012,1]]},"assertion":[{"value":"2012-04-05","order":0,"name":"received","label":"Received","group":{"name":"publication_history","label":"Publication History"}},{"value":"2012-05-10","order":1,"name":"accepted","label":"Accepted","group":{"name":"publication_history","label":"Publication History"}},{"value":"2012-07-05","order":2,"name":"published","label":"Published","group":{"name":"publication_history","label":"Publication History"}}],"article-number":"859492"}}