{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,7,30]],"date-time":"2025-07-30T13:13:43Z","timestamp":1753881223163,"version":"3.41.2"},"reference-count":11,"publisher":"Wiley","issue":"1","license":[{"start":{"date-parts":[[2012,7,12]],"date-time":"2012-07-12T00:00:00Z","timestamp":1342051200000},"content-version":"vor","delay-in-days":193,"URL":"http:\/\/creativecommons.org\/licenses\/by\/3.0\/"}],"funder":[{"name":"Thailand\u2019s Office of the Higher Education Commission","award":["55000613"],"award-info":[{"award-number":["55000613"]}]}],"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>This paper deals with new methods for approximating a solution to the fixed point problem; find , where <jats:italic>H<\/jats:italic> is a Hilbert space, <jats:italic>C<\/jats:italic> is a closed convex subset of <jats:italic>H<\/jats:italic>, <jats:italic>f<\/jats:italic> is a <jats:italic>\u03c1<\/jats:italic>\u2010contraction from <jats:italic>C<\/jats:italic> into <jats:italic>H<\/jats:italic>, 0 &lt; <jats:italic>\u03c1<\/jats:italic> &lt; 1, <jats:italic>A<\/jats:italic> is a strongly positive linear\u2010bounded operator with coefficient , , <jats:italic>T<\/jats:italic> is a nonexpansive mapping on <jats:italic>C,<\/jats:italic> and <jats:italic>P<\/jats:italic><jats:sub><jats:italic>F<\/jats:italic>(<jats:italic>T<\/jats:italic>)<\/jats:sub> denotes the metric projection on the set of fixed point of <jats:italic>T<\/jats:italic>. Under a suitable different parameter, we obtain strong convergence theorems by using the projection method which solves the variational inequality  for <jats:italic>x<\/jats:italic> \u2208 <jats:italic>F<\/jats:italic>(<jats:italic>T<\/jats:italic>), where <jats:italic>\u03c4<\/jats:italic> \u2208 [0, <jats:italic>\u221e<\/jats:italic>). Our results generalize and improve the corresponding results of Yao et al. (2010) and some authors. Furthermore, we give an example which supports our main theorem in the last part.<\/jats:p>","DOI":"10.1155\/2012\/174318","type":"journal-article","created":{"date-parts":[[2012,7,13]],"date-time":"2012-07-13T17:03:48Z","timestamp":1342199028000},"update-policy":"https:\/\/doi.org\/10.1002\/crossmark_policy","source":"Crossref","is-referenced-by-count":2,"title":["General Iterative Algorithms for Hierarchical Fixed Points Approach to Variational Inequalities"],"prefix":"10.1155","volume":"2012","author":[{"given":"Nopparat","family":"Wairojjana","sequence":"first","affiliation":[]},{"given":"Poom","family":"Kumam","sequence":"additional","affiliation":[]}],"member":"311","published-online":{"date-parts":[[2012,7,12]]},"reference":[{"key":"e_1_2_5_1_2","doi-asserted-by":"publisher","DOI":"10.1080\/01630569808816813"},{"key":"e_1_2_5_2_2","doi-asserted-by":"publisher","DOI":"10.1080\/01630569808816822"},{"key":"e_1_2_5_3_2","doi-asserted-by":"publisher","DOI":"10.1016\/S1570-579X(01)80028-8"},{"key":"e_1_2_5_4_2","doi-asserted-by":"publisher","DOI":"10.1112\/S0024610702003332"},{"key":"e_1_2_5_5_2","doi-asserted-by":"publisher","DOI":"10.1023\/A:1023073621589"},{"key":"e_1_2_5_6_2","doi-asserted-by":"publisher","DOI":"10.1006\/jmaa.1999.6615"},{"key":"e_1_2_5_7_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.jmaa.2004.04.059"},{"key":"e_1_2_5_8_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.jmaa.2005.05.028"},{"key":"e_1_2_5_9_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.mcm.2010.06.038"},{"key":"e_1_2_5_10_2","first-page":"78","volume-title":"Proceedings of Symposia in Pure Mathematics","author":"Browder F. E.","year":"1976"},{"key":"e_1_2_5_11_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.na.2006.08.036"}],"container-title":["Journal of Applied Mathematics"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/downloads.hindawi.com\/journals\/jam\/2012\/174318.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/downloads.hindawi.com\/journals\/jam\/2012\/174318.xml","content-type":"application\/xml","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/pdf\/10.1155\/2012\/174318","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2024,6,11]],"date-time":"2024-06-11T07:03:03Z","timestamp":1718089383000},"score":1,"resource":{"primary":{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/10.1155\/2012\/174318"}},"subtitle":[],"editor":[{"given":"Zhenyu","family":"Huang","sequence":"additional","affiliation":[]}],"short-title":[],"issued":{"date-parts":[[2012,1]]},"references-count":11,"journal-issue":{"issue":"1","published-print":{"date-parts":[[2012,1]]}},"alternative-id":["10.1155\/2012\/174318"],"URL":"https:\/\/doi.org\/10.1155\/2012\/174318","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":"2012-03-24","order":0,"name":"received","label":"Received","group":{"name":"publication_history","label":"Publication History"}},{"value":"2012-05-16","order":1,"name":"accepted","label":"Accepted","group":{"name":"publication_history","label":"Publication History"}},{"value":"2012-07-12","order":2,"name":"published","label":"Published","group":{"name":"publication_history","label":"Publication History"}}],"article-number":"174318"}}