Strong convergence theorems for quasi-nonexpansive mappings and maximal monotone operators in Hilbert spaces

被引：0

作者：

Huan-chun Wu

Cao-zong Cheng

De-ning Qu

机构：

[1] Beijing University of Technology,College of Applied Sciences

来源：

Journal of Inequalities and Applications | / 2014卷

关键词：

quasi-nonexpansive mapping; maximal monotone operator; variational inequality;

D O I：

暂无

中图分类号：

学科分类号：

摘要：

We present the strong convergence theorem for the iterative scheme for finding a common element of the fixed-point set of a quasi-nonexpansive mapping and the zero set of the sums of maximal monotone operators in Hilbert spaces. Our results extend and improve the recent results of Takahashi et al. (J. Optim. Theory Appl. 147:27-41, 2010) and Takahashi and Takahashi (Nonlinear Anal. 69:1025-1033, 2008).

引用

共 50 条

[1] Strong convergence theorems for quasi-nonexpansive mappings and maximal monotone operators in Hilbert spaces
Wu, Huan-chun
Cheng, Cao-zong
Qu, De-ning
[J]. JOURNAL OF INEQUALITIES AND APPLICATIONS, 2014,
[2] Weak and Strong Convergence Theorems of Quasi-Nonexpansive Mappings in a Hilbert Spaces
Gang Eun Kim
[J]. Journal of Optimization Theory and Applications, 2012, 152 : 727 - 738
[3] Weak and Strong Convergence Theorems of Quasi-Nonexpansive Mappings in a Hilbert Spaces
Kim, Gang Eun
[J]. JOURNAL OF OPTIMIZATION THEORY AND APPLICATIONS, 2012, 152 (03) : 727 - 738
[4] Strong Convergence Theorems for Maximal Monotone Operators with Nonlinear Mappings in Hilbert Spaces
S. Takahashi
W. Takahashi
M. Toyoda
[J]. Journal of Optimization Theory and Applications, 2010, 147 : 27 - 41
[5] Strong Convergence Theorems for Maximal Monotone Operators with Nonlinear Mappings in Hilbert Spaces
Takahashi, S.
Takahashi, W.
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[J]. JOURNAL OF OPTIMIZATION THEORY AND APPLICATIONS, 2010, 147 (01) : 27 - 41
[6] STRONG CONVERGENCE THEOREMS FOR MAXIMAL MONOTONE OPERATORS AND GENERALIZED NONEXPANSIVE MAPPINGS IN BANACH SPACES
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[J]. JOURNAL OF NONLINEAR AND CONVEX ANALYSIS, 2010, 11 (01) : 45 - 63
[7] Strong convergence for maximal monotone operators, relatively quasi-nonexpansive mappings, variational inequalities and equilibrium problems
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Poom Kumam
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[J]. Journal of Global Optimization, 2013, 57 : 1299 - 1318
[8] Strong convergence for maximal monotone operators, relatively quasi-nonexpansive mappings, variational inequalities and equilibrium problems
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[J]. JOURNAL OF GLOBAL OPTIMIZATION, 2013, 57 (04) : 1299 - 1318
[9] On Strong Convergence of Halpern's Method for Quasi-Nonexpansive Mappings in Hilbert Spaces
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Llorens-Fuster, Enrique
Marino, Giuseppe
Rugiano, Angela
[J]. MATHEMATICAL MODELLING AND ANALYSIS, 2016, 21 (01) : 63 - 82
[10] Strong Convergence Theorems by Hybrid Methods for Maximal Monotone Operators and Relatively Nonexpansive Mappings in Banach Spaces
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[J]. JOURNAL OF CONVEX ANALYSIS, 2009, 16 (3-4) : 791 - 806

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