标题:Necessary and Sufficient Condition for Mann Iteration Converges to a Fixed Point of Lipschitzian Mappings
作者:Xiang, Chang-He; Zhang, Jiang-Hua; Chen, Zhe
作者机构:[Zhang, Jiang-Hua] Shandong Univ, Sch Management, Jinan 250100, Shandong, Peoples R China.; [Xiang, Chang-He; Chen, Zhe] Chongqing Normal Univ, Coll 更多
通讯作者:Zhang, JH
通讯作者地址:[Zhang, JH]Shandong Univ, Sch Management, Jinan 250100, Shandong, Peoples R China.
来源:JOURNAL OF APPLIED MATHEMATICS
出版年:2012
DOI:10.1155/2012/327878
摘要:Suppose that E is a real normed linear space, C is a nonempty convex subset of E, T : C -> C is a Lipschitzian mapping, and x* is an element of C is a fixed point of T. For given x(0) is an element of C, suppose that the sequence {x(n)} subset of C is the Mann iterative sequence defined by x(n+1) = (1 - alpha(n))x(n) + alpha(n)Tx(n), n >= 0, where {alpha(n)} is a sequence in [0, 1], Sigma(infinity)(n=0)alpha(2)(n) < infinity, Sigma(infinity)(n=0)alpha(n) = infinity. We prove that the sequence {x(n)} strongly converges to x* if and only if there exists a strictly increasing function Phi : [0, infinity)-> [0, infinity) with Phi(0) = 0 such that lim sup(n ->infinity) in fj((xn-x*) is an element of J(xn-x*)) {< Tx(n) - x*, j(x(n) - x*)> - parallel to x(n) - x*parallel to(2) + Phi parallel to xn - x*parallel to)} <= 0.
收录类别:SCOPUS;SCIE
资源类型:期刊论文
原文链接:https://www.scopus.com/inward/record.uri?eid=2-s2.0-84874848233&doi=10.1155%2f2012%2f327878&partnerID=40&md5=fa995fdce4aeaaae43361933e6c32928
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