An extragradient-like approximation method for variational inequalities and fixed point problems

被引：0
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作者：
Lu-Chuan Ceng
Qamrul Hasan Ansari
Ngai-Ching Wong
Jen-Chih Yao
机构：
[1] Shanghai Normal University,Department of Mathematics
[2] Scientific Computing Key Laboratory Of Shanghai Universities,Department of Mathematics
[3] Aligarh Muslim University,Department of Applied Mathematics
[4] National Sun Yat-Sen University,Center for General Education
[5] Kaohsiung Medical University,undefined
来源：
Fixed Point Theory and Applications | / 2011卷
关键词：
extragradient-like approximation method; modified Mann iteration process; variational inequality; asymptotically strict pseudocontractive mapping in the intermediate sense; fixed point; monotone mapping; strong convergence; demiclosedness principle;
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摘要：
The purpose of this paper is to investigate the problem of finding a common element of the set of fixed points of an asymptotically strict pseudocontractive mapping in the intermediate sense and the set of solutions of a variational inequality problem for a monotone and Lipschitz continuous mapping. We introduce an extragradient-like iterative algorithm that is based on the extragradient-like approximation method and the modified Mann iteration process. We establish a strong convergence theorem for two sequences generated by this extragradient-like iterative algorithm. Utilizing this theorem, we also design an iterative process for finding a common fixed point of two mappings, one of which is an asymptotically strict pseudocontractive mapping in the intermediate sense and the other taken from the more general class of Lipschitz pseudocontractive mappings.
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