| Banach空间中集值平衡问题解的迭代算法 |
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| 引用本文： | 汪裕才.Banach空间中集值平衡问题解的迭代算法[J].四川师范大学学报(自然科学版),2010,33(6). |
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| 作者姓名： | 汪裕才 |
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| 作者单位： | 四川师范大学计算机科学学院; |
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| 基金项目： | 四川省教育厅自然科学重点基金 |
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| 摘 要： | 在自反Banach空间中研究了集值平衡问题解的存在性和迭代算法.首先,给出了伪单调集值映射的定义,并将该定义与已有的伪单调单值映射的定义进行了比较.其次,应用KKM定理证明了集值平衡问题解的存在性.然后,利用辅助原理,构造了集值平衡问题解的迭代算法,还应用KKM定理证明了辅助变分不等式解的存在性.最后,在集值映射是伪单调的假设条件下证明了迭代序列的收敛性.推广和统一了最近一些文献上的相关结果.
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| 关 键 词： | 集值平衡问题 迭代算法 伪单调映射 强凸泛函 |
Iterative Schemes for Solving Multivalued Equilibrium Problem in Banach Spaces |
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| WANG Yu-cai.Iterative Schemes for Solving Multivalued Equilibrium Problem in Banach Spaces[J].Journal of Sichuan Normal University(Natural Science),2010,33(6). |
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| Authors: | WANG Yu-cai |
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| Institution: | WANG Yu-cai(College of Computer Science,Sichuan Normal University,Chengdu 610066,Sichuan) |
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| Abstract: | In this paper,we introduce the concept of pseudomonotonicity of a multivalued mapping and develop some iterative schemes for finding the approximate solutions of multivalued equilibrium problem in reflexive Banach spaces.We use the concept of pseudomonotonicity to prove the convergence of the approximate solutions to the exact solution of multivalued equilibrium problem.It is worth notice that we do not assume Lipschitz continuity of any mappings in this paper. |
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| Keywords: | multivalued equilibrium problems iterative schemes pseudomonotone strongly convex functions Banach space |
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