{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,7,30]],"date-time":"2025-07-30T14:45:17Z","timestamp":1753886717165,"version":"3.41.2"},"reference-count":14,"publisher":"Wiley","issue":"1","license":[{"start":{"date-parts":[[2012,2,22]],"date-time":"2012-02-22T00:00:00Z","timestamp":1329868800000},"content-version":"vor","delay-in-days":52,"URL":"http:\/\/creativecommons.org\/licenses\/by\/3.0\/"}],"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>X<\/jats:italic> be a uniformly convex Banach space and <jats:italic>\ud835\udcae<\/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>} be a nonexpansive semigroup such that <jats:italic>F<\/jats:italic>(<jats:italic>\ud835\udcae<\/jats:italic>) = \u22c2<jats:sub><jats:italic>s<\/jats:italic>&gt;0<\/jats:sub><jats:italic>F<\/jats:italic>(<jats:italic>T<\/jats:italic>(<jats:italic>s<\/jats:italic>)) \u2260 <jats:italic>\u2205<\/jats:italic>. Consider the iterative method that generates the sequence {<jats:italic>x<\/jats:italic><jats:sub><jats:italic>n<\/jats:italic><\/jats:sub>} by the algorithm , where {<jats:italic>\u03b1<\/jats:italic><jats:sub><jats:italic>n<\/jats:italic><\/jats:sub>}, {<jats:italic>\u03b2<\/jats:italic><jats:sub><jats:italic>n<\/jats:italic><\/jats:sub>}, and {<jats:italic>s<\/jats:italic><jats:sub><jats:italic>n<\/jats:italic><\/jats:sub>} are three sequences satisfying certain conditions, <jats:italic>f<\/jats:italic> : <jats:italic>C<\/jats:italic> \u2192 <jats:italic>C<\/jats:italic> is a contraction mapping. Strong convergence of the algorithm {<jats:italic>x<\/jats:italic><jats:sub><jats:italic>n<\/jats:italic><\/jats:sub>} is proved assuming <jats:italic>X<\/jats:italic> either has a weakly continuous duality map or has a uniformly G\u00e2teaux differentiable norm.<\/jats:p>","DOI":"10.1155\/2012\/641479","type":"journal-article","created":{"date-parts":[[2012,2,22]],"date-time":"2012-02-22T21:03:13Z","timestamp":1329944593000},"update-policy":"https:\/\/doi.org\/10.1002\/crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Strong Convergence Theorems for Nonexpansive Semigroups and Variational Inequalities in Banach Spaces"],"prefix":"10.1155","volume":"2012","author":[{"given":"Haiqing","family":"Wang","sequence":"first","affiliation":[]},{"given":"Yongfu","family":"Su","sequence":"additional","affiliation":[]},{"given":"Hong","family":"Zhang","sequence":"additional","affiliation":[]}],"member":"311","published-online":{"date-parts":[[2012,2,22]]},"reference":[{"key":"e_1_2_7_1_2","doi-asserted-by":"publisher","DOI":"10.1073\/pnas.53.6.1272"},{"key":"e_1_2_7_2_2","doi-asserted-by":"publisher","DOI":"10.1016\/0022-247X(80)90323-6"},{"key":"e_1_2_7_3_2","doi-asserted-by":"publisher","DOI":"10.1007\/BF00251595"},{"key":"e_1_2_7_4_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.jmaa.2007.05.021"},{"key":"e_1_2_7_5_2","doi-asserted-by":"publisher","DOI":"10.1006\/jmaa.1999.6615"},{"key":"e_1_2_7_6_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.jmaa.2004.04.059"},{"key":"e_1_2_7_7_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.mcm.2007.10.002"},{"key":"e_1_2_7_8_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.cam.2006.01.009"},{"volume-title":"Nonlinear Functional Analysis\u2014Fixed Point Theory and Its Applications","year":"2000","author":"Takahashi W.","key":"e_1_2_7_9_2"},{"key":"e_1_2_7_10_2","series-title":"Monographs and Textbooks in Pure and Applied Mathematics","volume-title":"Uniform Convexity, Hyperbolic Geometry, and Nonexpansive Mappings","author":"Goebel K.","year":"1984"},{"key":"e_1_2_7_11_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.jmaa.2005.04.082"},{"key":"e_1_2_7_12_2","doi-asserted-by":"publisher","DOI":"10.1090\/S0002-9904-1968-11983-4"},{"key":"e_1_2_7_13_2","doi-asserted-by":"publisher","DOI":"10.1007\/BF01109805"},{"key":"e_1_2_7_14_2","doi-asserted-by":"publisher","DOI":"10.1016\/0022-247X(84)90019-2"}],"container-title":["Journal of Applied Mathematics"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/downloads.hindawi.com\/journals\/jam\/2012\/641479.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/downloads.hindawi.com\/journals\/jam\/2012\/641479.xml","content-type":"application\/xml","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/pdf\/10.1155\/2012\/641479","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2024,6,11]],"date-time":"2024-06-11T07:18:15Z","timestamp":1718090295000},"score":1,"resource":{"primary":{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/10.1155\/2012\/641479"}},"subtitle":[],"editor":[{"given":"Rudong","family":"Chen","sequence":"additional","affiliation":[]}],"short-title":[],"issued":{"date-parts":[[2012,1]]},"references-count":14,"journal-issue":{"issue":"1","published-print":{"date-parts":[[2012,1]]}},"alternative-id":["10.1155\/2012\/641479"],"URL":"https:\/\/doi.org\/10.1155\/2012\/641479","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":"2011-11-11","order":0,"name":"received","label":"Received","group":{"name":"publication_history","label":"Publication History"}},{"value":"2011-12-17","order":1,"name":"accepted","label":"Accepted","group":{"name":"publication_history","label":"Publication History"}},{"value":"2012-02-22","order":2,"name":"published","label":"Published","group":{"name":"publication_history","label":"Publication History"}}],"article-number":"641479"}}