Convergence of a Multistep Ishikawa Iteration Algorithm for a Finite Family of Lipschitz Mappings and Its Applications
Received:March 24, 2012  Revised:November 22, 2012
Key Words: convex feasibility problem   common fixed point problem   Lipschitz mappings.  
Fund Project:Supported by the National Natural Science Foundation of China (Grant No.11201216), the Natural Science Foundations of Jiangxi Province (Grant No.20114BAB201004) and the Youth Science Funds of The Education Department of Jiangxi Province (Grant No.GJJ12141).
Author NameAffiliation
Yuchao TANG Department of Mathematics, Nanchang University, Jiangxi 330031, P. R. China会Department of Mathematics, Xi'an Jiaotong University, Shaanxi 710049, P. R. China 
Chuanxi ZHU Department of Mathematics, Nanchang University, Jiangxi 330031, P. R. China 
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      The purpose of this paper is to investigate the problem of finding a common fixed point of Lipschitz mappings. We introduce a multistep Ishikawa iteration approximation method which is based upon the Ishikawa iteration method and the Noor iteration method, and we prove some necessary and sufficient conditions for the strong convergence of the iteration scheme to a common fixed point of a finite family of quasi-Lipschitz mappings and pseudocontractive mappings, respectively. In particular, we establish a strong convergence theorem of the sequence generated by the multistep Ishikawa scheme to a common fixed point of nonexpansive mappings. As applications, some numerical experiments of the multistep Ishikawa iteration algorithm are given to demonstrate the convergence results.
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