Strong Convergence Theorems for Variational Inequalities and Fixed Point Problems of Asymptotically Strict Pseudocontractive Mappings in the Intermediate Sense

被引：0
作者：
Lu-Chuan Ceng
Jen-Chih Yao
机构：
[1] Shanghai Normal University,Department of Mathematics
[2] Scientific Computing Key Laboratory of Shanghai Universities,Center for General Education
[3] Kaohsiung Medical University,undefined
来源：
Acta Applicandae Mathematicae | 2011年 / 115卷
关键词：
Modified hybrid Mann iterative scheme with perturbed mapping; Variational inequality; Asymptotically strict pseudocontractive mapping in the intermediate sense; Fixed point; Monotone mapping; Strong convergence; Demiclosedness principle; 47H09; 47J20;
D O I：
暂无
中图分类号：
学科分类号：
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 the variational inequality problem for a monotone, Lipschitz continuous mapping. We introduce a modified hybrid Mann iterative scheme with perturbed mapping which is based on well-known CQ method, Mann iteration method and hybrid (or outer approximation) method. We establish a strong convergence theorem for three sequences generated by this modified hybrid Mann iterative scheme with perturbed mapping. 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.
引用
收藏
页码：167 / 191
页数：24
相关论文
共 99 条
[1]  
Agarwal R.P.(2007)Iterative construction of fixed points of nearly asymptotically nonexpansive mappings J. Nonlinear Convex Anal. 8 61-79
[2]  
O’Regan D.(2000)Methods for solving variational inequalities with related constraints Comput. Math. Math. Phys. 40 1239-1254
[3]  
Sahu D.R.(2004)Regularized prediction method for solving variational inequalities with an inexactly given set Comput. Math. Math. Phys. 44 750-758
[4]  
Antipin A.S.(1993)Convergence of iterates of asymptotically nonexpansive mappings in Banach spaces with the uniform Opial property Colloq. Math. 65 169-179
[5]  
Antipin A.S.(2005)An outer approximation method for the variational inequality problem SIAM J. Control Optim. 43 2071-2088
[6]  
Vasiliev F.P.(2007)An extragradient-like approximation method for variational inequality problems and fixed point problems Appl. Math. Comput. 190 205-215
[7]  
Bruck R.E.(2008)Mixed projection methods for systems of variational inequalities J. Glob. Optim. 41 465-478
[8]  
Kuczumow T.(2008)Relaxed viscosity approximation methods for fixed point problems and variational inequality problems Nonlinear Anal., Theory Methods Appl. 69 3299-3309
[9]  
Reich S.(2010)Convergence analysis of a hybrid Mann iterative scheme with perturbed mapping for variational inequalities and fixed point problems Optimization 29 987-1033
[10]  
Burachik R.S.(2008)Mann type steepest-descent and modified hybrid steepest-descent methods for variational inequalities in Banach spaces Numer. Funct. Anal. Optim. 12 227-244
12345678910