Convergence theorems for finding zero points of maximal monotone operators and equilibrium problems in Banach spaces

被引：0

作者：

Siwaporn Saewan

Poom Kumam

Yeol Je Cho

机构：

[1] Thaksin University (TSU),Department of Mathematics and Statistics, Faculty of Science

[2] King Mongkut’s University of Technology Thonburi (KMUTT),Department of Mathematics, Faculty of Science

[3] Gyeongsang National University,Department of Mathematics Education and RINS

来源：

Journal of Inequalities and Applications | / 2013卷 / 1期

关键词：

maximal monotone operators; hybrid projection method; system of generalized equilibrium problems;

D O I：

暂无

中图分类号：

学科分类号：

摘要：

In this paper, we construct a new hybrid projection method for approximating a common element of the set of zeroes of a finite family of maximal monotone operators and the set of common solutions to a system of generalized equilibrium problems in a uniformly smooth and strictly convex Banach space. We prove strong convergence theorems of the algorithm to a common element of these two sets. As application, we also apply our results to find common solutions of variational inequalities and zeroes of maximal monotone operators.

引用

共 50 条

[1] Convergence theorems for finding zero points of maximal monotone operators and equilibrium problems in Banach spaces
Saewan, Siwaporn
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Cho, Yeol Je
[J]. JOURNAL OF INEQUALITIES AND APPLICATIONS, 2013,
[2] Convergence theorems for maximal monotone operators and fixed point problems in Banach spaces
Shehu, Yekini
[J]. APPLIED MATHEMATICS AND COMPUTATION, 2014, 239 : 285 - 298
[3] Strong convergence theorems for maximal monotone operators in Banach spaces
Ceng, L. C.
Schaible, S.
Yao, J. C.
[J]. OPTIMIZATION, 2010, 59 (06) : 807 - 819
[4] NONLINEAR OPERATORS OF MONOTONE TYPE AND CONVERGENCE THEOREMS WITH EQUILIBRIUM PROBLEMS IN BANACH SPACES
Takahashi, Wataru
Yao, Jen-Chih
[J]. TAIWANESE JOURNAL OF MATHEMATICS, 2011, 15 (02): : 787 - 818
[5] Strong convergence theorems for resolvents of maximal monotone operators in Banach spaces
Shigeo Ohsawa
Wataru Takahashi
[J]. Archiv der Mathematik, 2003, 81 : 439 - 445
[6] Strong　Convergence　Theorems　for　Perturbed　Maximal　Monotone　Operators　in　Banach　Spaces
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赵义纯
[J]. Communications in Mathematical Research, 1995, (01) : 75 - 78
[7] Strong convergence theorems for resolvents of maximal monotone operators in Banach spaces
Ohsawa, S
Takahashi, W
[J]. ARCHIV DER MATHEMATIK, 2003, 81 (04) : 439 - 445
[8] WEAK AND STRONG CONVERGENCE THEOREMS OF PROXIMAL POINT ALGORITHM FOR SOLVING GENERALIZED MIXED EQUILIBRIUM PROBLEMS AND FINDING ZEROES OF MAXIMAL MONOTONE OPERATORS IN BANACH SPACES
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[9] 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
[10] STRONG CONVERGENCE THEOREMS FOR GENERALIZED SPLIT EQUILIBRIUM PROBLEMS AND MAXIMAL MONOTONE OPERATORS
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