{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,7,30]],"date-time":"2025-07-30T14:38:31Z","timestamp":1753886311754,"version":"3.41.2"},"reference-count":18,"publisher":"Wiley","issue":"1","license":[{"start":{"date-parts":[[2012,2,20]],"date-time":"2012-02-20T00:00:00Z","timestamp":1329696000000},"content-version":"vor","delay-in-days":50,"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":["11126334","11071169","Y6110287"],"award-info":[{"award-number":["11126334","11071169","Y6110287"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["11126334","11071169","Y6110287"],"award-info":[{"award-number":["11126334","11071169","Y6110287"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100004731","name":"Natural Science Foundation of Zhejiang Province","doi-asserted-by":"publisher","award":["11126334","11071169","Y6110287"],"award-info":[{"award-number":["11126334","11071169","Y6110287"]}],"id":[{"id":"10.13039\/501100004731","id-type":"DOI","asserted-by":"publisher"}]}],"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>Let <jats:italic>H<\/jats:italic> be a real Hilbert space. Consider on <jats:italic>H<\/jats:italic> a nonexpansive semigroup <jats:italic>S<\/jats:italic> = {<jats:italic>T<\/jats:italic>(<jats:italic>s<\/jats:italic>) : 0 \u2264 <jats:italic>s<\/jats:italic> &lt; <jats:italic>\u221e<\/jats:italic>} with a common fixed point, a contraction <jats:italic>f<\/jats:italic> with the coefficient 0 &lt; <jats:italic>\u03b1<\/jats:italic> &lt; 1, and a strongly positive linear bounded self\u2010adjoint operator <jats:italic>A<\/jats:italic> with the coefficient &gt;\u2009\u20090. Let \/<jats:italic>\u03b1<\/jats:italic>. It is proved that the sequence {<jats:italic>x<\/jats:italic><jats:sub><jats:italic>n<\/jats:italic><\/jats:sub>} generated by the iterative method  converges strongly to a common fixed point <jats:italic>x<\/jats:italic><jats:sup>*<\/jats:sup> \u2208 <jats:italic>F<\/jats:italic>(<jats:italic>S<\/jats:italic>), where <jats:italic>F<\/jats:italic>(<jats:italic>S<\/jats:italic>) denotes the common fixed point of the nonexpansive semigroup. The point <jats:italic>x<\/jats:italic><jats:sup>*<\/jats:sup> solves the variational inequality \u2329(<jats:italic>\u03b3<\/jats:italic><jats:italic>f<\/jats:italic> \u2212 <jats:italic>A<\/jats:italic>)<jats:italic>x<\/jats:italic><jats:sup>*<\/jats:sup>, <jats:italic>x<\/jats:italic> \u2212 <jats:italic>x<\/jats:italic><jats:sup>*<\/jats:sup>\u232a\u22640 for all <jats:italic>x<\/jats:italic> \u2208 <jats:italic>F<\/jats:italic>(<jats:italic>S<\/jats:italic>).<\/jats:p>","DOI":"10.1155\/2012\/417234","type":"journal-article","created":{"date-parts":[[2012,2,20]],"date-time":"2012-02-20T21:02:20Z","timestamp":1329771740000},"update-policy":"https:\/\/doi.org\/10.1002\/crossmark_policy","source":"Crossref","is-referenced-by-count":1,"title":["Approximation of Common Fixed Points of Nonexpansive Semigroups in Hilbert Spaces"],"prefix":"10.1155","volume":"2012","author":[{"given":"Dan","family":"Zhang","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Xiaolong","family":"Qin","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Feng","family":"Gu","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"311","published-online":{"date-parts":[[2012,2,20]]},"reference":[{"key":"e_1_2_4_1_2","doi-asserted-by":"publisher","DOI":"10.1073\/pnas.54.4.1041"},{"key":"e_1_2_4_2_2","doi-asserted-by":"publisher","DOI":"10.1007\/BF00251595"},{"key":"e_1_2_4_3_2","doi-asserted-by":"publisher","DOI":"10.1016\/0022-247X(80)90323-6"},{"key":"e_1_2_4_4_2","doi-asserted-by":"publisher","DOI":"10.1090\/S0002-9904-1967-11864-0"},{"key":"e_1_2_4_5_2","first-page":"A1357","article-title":"Approximation de points fixes de contractions","volume":"284","author":"Lions P.-L.","year":"1977","journal-title":"Comptes Rendus de l\u2032Acad\u00e9mie des Sciences"},{"key":"e_1_2_4_6_2","doi-asserted-by":"publisher","DOI":"10.1007\/BF01190119"},{"key":"e_1_2_4_7_2","doi-asserted-by":"publisher","DOI":"10.1080\/01630569808816813"},{"key":"e_1_2_4_8_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.na.2008.04.007"},{"key":"e_1_2_4_9_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.jmaa.2005.05.028"},{"key":"e_1_2_4_10_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.camwa.2008.10.073"},{"key":"e_1_2_4_11_2","doi-asserted-by":"publisher","DOI":"10.1023\/A:1023073621589"},{"key":"e_1_2_4_12_2","doi-asserted-by":"publisher","DOI":"10.1112\/S0024610702003332"},{"key":"e_1_2_4_13_2","doi-asserted-by":"publisher","DOI":"10.1080\/01630569808816822"},{"key":"e_1_2_4_14_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.mcm.2007.10.002"},{"key":"e_1_2_4_15_2","doi-asserted-by":"publisher","DOI":"10.1016\/S0362-546X(97)00682-2"},{"key":"e_1_2_4_16_2","doi-asserted-by":"publisher","DOI":"10.1006\/jmaa.1997.5398"},{"key":"e_1_2_4_17_2","doi-asserted-by":"publisher","DOI":"10.1017\/CBO9780511526152"},{"volume-title":"Iterative Methods for Nonlinear Operator Equations in Banach Spaces","year":"2002","author":"Chang S.-S.","key":"e_1_2_4_18_2"}],"container-title":["Journal of Applied Mathematics"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/downloads.hindawi.com\/journals\/jam\/2012\/417234.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/downloads.hindawi.com\/journals\/jam\/2012\/417234.xml","content-type":"application\/xml","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/pdf\/10.1155\/2012\/417234","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2024,6,11]],"date-time":"2024-06-11T07:07:21Z","timestamp":1718089641000},"score":1,"resource":{"primary":{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/10.1155\/2012\/417234"}},"subtitle":[],"editor":[{"given":"Rudong","family":"Chen","sequence":"additional","affiliation":[],"role":[{"role":"editor","vocabulary":"crossref"}]}],"short-title":[],"issued":{"date-parts":[[2012,1]]},"references-count":18,"journal-issue":{"issue":"1","published-print":{"date-parts":[[2012,1]]}},"alternative-id":["10.1155\/2012\/417234"],"URL":"https:\/\/doi.org\/10.1155\/2012\/417234","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":"2011-10-14","order":0,"name":"received","label":"Received","group":{"name":"publication_history","label":"Publication History"}},{"value":"2011-12-11","order":1,"name":"accepted","label":"Accepted","group":{"name":"publication_history","label":"Publication History"}},{"value":"2012-02-20","order":2,"name":"published","label":"Published","group":{"name":"publication_history","label":"Publication History"}}],"article-number":"417234"}}