{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,7,30]],"date-time":"2025-07-30T13:14:35Z","timestamp":1753881275491,"version":"3.41.2"},"reference-count":25,"publisher":"Wiley","issue":"1","license":[{"start":{"date-parts":[[2012,3,25]],"date-time":"2012-03-25T00:00:00Z","timestamp":1332633600000},"content-version":"vor","delay-in-days":84,"URL":"http:\/\/creativecommons.org\/licenses\/by\/3.0\/"}],"funder":[{"DOI":"10.13039\/501100012226","name":"Fundamental Research Funds for the Central Universities","doi-asserted-by":"crossref","award":["ZXH2011D005"],"award-info":[{"award-number":["ZXH2011D005"]}],"id":[{"id":"10.13039\/501100012226","id-type":"DOI","asserted-by":"crossref"}]}],"content-domain":{"domain":["onlinelibrary.wiley.com"],"crossmark-restriction":true},"short-container-title":["Journal of Applied Mathematics"],"published-print":{"date-parts":[[2012,1]]},"abstract":"Let C<\/jats:italic> be a nonempty closed convex subset of a real uniformly smooth Banach space X<\/jats:italic>, an infinite family of nonexpansive mappings with the nonempty set of common fixed points , and f<\/jats:italic> : C<\/jats:italic> \u2192 C<\/jats:italic> a contraction. We introduce an explicit iterative algorithm x<\/jats:italic>n<\/jats:italic>+1<\/jats:sub> = \u03b1<\/jats:italic>n<\/jats:italic><\/jats:sub>f<\/jats:italic>(x<\/jats:italic>n<\/jats:italic><\/jats:sub>)+(1 \u2212 \u03b1<\/jats:italic>n<\/jats:italic><\/jats:sub>)L<\/jats:italic>n<\/jats:italic><\/jats:sub>x<\/jats:italic>n<\/jats:italic><\/jats:sub>, where \n\t\t\t\t\t\t and w<\/jats:italic>k<\/jats:italic><\/jats:sub> > 0 with . Under certain appropriate conditions on {\u03b1<\/jats:italic>n<\/jats:italic><\/jats:sub>}, we prove that {x<\/jats:italic>n<\/jats:italic><\/jats:sub>} converges strongly to a common fixed point x<\/jats:italic>*<\/jats:sup> of , which solves the following variational inequality: , where J<\/jats:italic> is the (normalized) duality mapping of X<\/jats:italic>. This algorithm is brief and needs less computational work, since it does not involve W<\/jats:italic>\u2010mapping.<\/jats:p>","DOI":"10.1155\/2012\/787419","type":"journal-article","created":{"date-parts":[[2012,3,25]],"date-time":"2012-03-25T21:02:22Z","timestamp":1332709342000},"update-policy":"https:\/\/doi.org\/10.1002\/crossmark_policy","source":"Crossref","is-referenced-by-count":4,"title":["Iterative Algorithm for Common Fixed Points of Infinite Family of Nonexpansive Mappings in Banach Spaces"],"prefix":"10.1155","volume":"2012","author":[{"given":"Songnian","family":"He","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Jun","family":"Guo","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"311","published-online":{"date-parts":[[2012,3,25]]},"reference":[{"key":"e_1_2_5_1_2","doi-asserted-by":"publisher","DOI":"10.1007\/BF00251595"},{"key":"e_1_2_5_2_2","doi-asserted-by":"publisher","DOI":"10.1073\/pnas.53.6.1272"},{"key":"e_1_2_5_3_2","doi-asserted-by":"publisher","DOI":"10.1090\/S0002-9904-1967-11864-0"},{"key":"e_1_2_5_4_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\u2014Series A-B"},{"key":"e_1_2_5_5_2","doi-asserted-by":"publisher","DOI":"10.1016\/0022-247X(80)90323-6"},{"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.2005.04.082"},{"key":"e_1_2_5_9_2","unstructured":"YaoY.andyaoyonghong@yahoo.cn ShahzadN. nshahzad@kau.edu.sa Strong convergence of a proximal point algorithm with general errors Optimization Letters. 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