{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2022,4,1]],"date-time":"2022-04-01T23:04:04Z","timestamp":1648854244467},"reference-count":23,"publisher":"Hindawi Limited","license":[{"start":{"date-parts":[[2014,1,1]],"date-time":"2014-01-01T00:00:00Z","timestamp":1388534400000},"content-version":"unspecified","delay-in-days":0,"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":["11071169","09ZZ133","20123127110002"],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Journal of Applied Mathematics"],"published-print":{"date-parts":[[2014]]},"abstract":"We introduce and analyze one iterative algorithm by hybrid shrinking projection method for finding a solution of the minimization problem for a convex and continuously Fr\u00e9chet differentiable functional, with constraints of several problems: finitely many generalized mixed equilibrium problems, finitely many variational inequalities, the general system of variational inequalities and the fixed point problem of an asymptotically strict pseudocontractive mapping in the intermediate sense in a real Hilbert space. We prove strong convergence theorem for the iterative algorithm under suitable conditions. On the other hand, we also propose another iterative algorithm by hybrid shrinking projection method for finding a fixed point of infinitely many nonexpansive mappings with the same constraints, and derive its strong convergence under mild assumptions.<\/jats:p>","DOI":"10.1155\/2014\/105928","type":"journal-article","created":{"date-parts":[[2014,5,8]],"date-time":"2014-05-08T21:09:38Z","timestamp":1399583378000},"page":"1-28","source":"Crossref","is-referenced-by-count":0,"title":["Convex Minimization with Constraints of Systems of Variational Inequalities, Mixed Equilibrium, Variational Inequality, and Fixed Point Problems"],"prefix":"10.1155","volume":"2014","author":[{"given":"Lu-Chuan","family":"Ceng","sequence":"first","affiliation":[{"name":"Department of Mathematics, Shanghai Normal University, and Scientific Computing Key Laboratory of Shanghai Universities, Shanghai 200234, China"}]},{"given":"Cheng-Wen","family":"Liao","sequence":"additional","affiliation":[{"name":"Department of Food and Beverage Management, Vanung University, Chung-Li 320061, Taiwan"}]},{"ORCID":"http:\/\/orcid.org\/0000-0001-5946-2304","authenticated-orcid":true,"given":"Chin-Tzong","family":"Pang","sequence":"additional","affiliation":[{"name":"Department of Information Management and Innovation Center for Big Data and Digital Convergence, Yuan Ze University, Chung-Li 32003, Taiwan"}]},{"ORCID":"http:\/\/orcid.org\/0000-0001-8900-761X","authenticated-orcid":true,"given":"Ching-Feng","family":"Wen","sequence":"additional","affiliation":[{"name":"Center for Fundamental Science, Kaohsiung Medical University, Kaohsiung 807, Taiwan"}]}],"member":"98","reference":[{"issue":"6","key":"1","doi-asserted-by":"crossref","first-page":"1401","DOI":"10.11650\/twjm\/1500405033","volume":"12","year":"2008","journal-title":"Taiwanese Journal of Mathematics"},{"key":"2","doi-asserted-by":"publisher","DOI":"10.1016\/j.jmaa.2008.02.041"},{"key":"3","doi-asserted-by":"publisher","DOI":"10.1016\/j.cam.2007.02.022"},{"key":"4","doi-asserted-by":"publisher","DOI":"10.1016\/j.na.2008.02.042"},{"key":"5","doi-asserted-by":"publisher","DOI":"10.1007\/s10957-009-9549-9"},{"key":"6","doi-asserted-by":"publisher","DOI":"10.1007\/s00186-007-0207-4"},{"key":"7","doi-asserted-by":"publisher","DOI":"10.1016\/S1570-579X(01)80028-8"},{"key":"8","doi-asserted-by":"publisher","DOI":"10.1186\/1687-1812-2012-92"},{"key":"9","doi-asserted-by":"publisher","DOI":"10.1016\/j.na.2007.02.029"},{"key":"10","doi-asserted-by":"publisher","DOI":"10.1016\/j.na.2008.07.007"},{"key":"11","doi-asserted-by":"publisher","DOI":"10.1155\/2011\/626159"},{"key":"12","doi-asserted-by":"publisher","DOI":"10.1007\/s10440-011-9614-x"},{"key":"13","doi-asserted-by":"publisher","DOI":"10.1080\/02331934.2010.527340"},{"key":"14","doi-asserted-by":"publisher","DOI":"10.1007\/s10957-011-9837-z"},{"key":"15","doi-asserted-by":"publisher","DOI":"10.1088\/0266-5611\/20\/1\/006"},{"key":"16","year":"1990"},{"key":"17","doi-asserted-by":"publisher","DOI":"10.1016\/j.na.2005.07.036"},{"key":"18","doi-asserted-by":"publisher","DOI":"10.1023\/B:JOTA.0000005048.79379.b6"},{"key":"19","doi-asserted-by":"publisher","DOI":"10.1016\/j.na.2005.08.018"},{"key":"20","volume":"2007, article 12","year":"2007","journal-title":"Fixed Point Theory and Applications"},{"key":"21","doi-asserted-by":"publisher","DOI":"10.1016\/j.cam.2013.01.004"},{"issue":"4","key":"22","first-page":"747","volume":"12","year":"1976","journal-title":"\u00c8konomika i Matematicheskie Metody"},{"key":"23","doi-asserted-by":"publisher","DOI":"10.1016\/j.na.2011.05.005"}],"container-title":["Journal of Applied Mathematics"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/downloads.hindawi.com\/journals\/jam\/2014\/105928.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/downloads.hindawi.com\/journals\/jam\/2014\/105928.xml","content-type":"application\/xml","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/downloads.hindawi.com\/journals\/jam\/2014\/105928.pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,8,10]],"date-time":"2019-08-10T09:07:13Z","timestamp":1565428033000},"score":1,"resource":{"primary":{"URL":"http:\/\/www.hindawi.com\/journals\/jam\/2014\/105928\/"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2014]]},"references-count":23,"alternative-id":["105928","105928"],"URL":"https:\/\/doi.org\/10.1155\/2014\/105928","relation":{},"ISSN":["1110-757X","1687-0042"],"issn-type":[{"value":"1110-757X","type":"print"},{"value":"1687-0042","type":"electronic"}],"subject":[],"published":{"date-parts":[[2014]]}}}