| Banach空间中一类广义均衡问题的收缩投影算法 |
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| 引用本文： | 陈玉清,黄建华.Banach空间中一类广义均衡问题的收缩投影算法[J].莆田学院学报,2013(5):9-13,17. |
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| 作者姓名： | 陈玉清 黄建华 |
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| 作者单位： | 福州大学数学与计算机科学学院,福建福州350108 |
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| 基金项目： | 福建省自然科学基金资助项目（2012J01005） |
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| 摘 要： | 在一致凸和一致光滑的Banach空间中,提出通过一种收缩投影算法来得到广义均衡问题解集EP,拟-φ-渐近非扩张算子的不动点集F(S)和极大单调算子T的零点解集T-10的公共解。在适当的条件下,证明了算法所产生的迭代序列强收敛于EP∩T-10∩F(S)中的某一点。
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| 关 键 词： | Banach空间 广义均衡问题 收缩投影算法 拟-φ-渐进非扩张算子 极大单调算子 迭代序列 |
A Shrinking Projection Method for a Type of Generalized Equilibrium Problems in Banach Spaces |
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| CHEN Yu-qing,HUANG Jian-hua.A Shrinking Projection Method for a Type of Generalized Equilibrium Problems in Banach Spaces[J].journal of putian university,2013(5):9-13,17. |
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| Authors: | CHEN Yu-qing HUANG Jian-hua |
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| Institution: | ( College of Mathematics and Computer Science, Fuzhou University, Fuzhou Fujian 350108, China ) |
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| Abstract: | In this paper, a shrinking projection method were proposed for finding a common element of the set EP of the solutions of a generalized equilibrium problem, the set F（S） of fixed points of a quasi-φ-asymptotically nonexpansive mapping and the set T-10 of zeros of a maximal monotone operator T in uniformly smooth and uniformly convex Banach spaces. It was proven that under appropriate conditions, the iterative sequence generated by the method converges strongly to some point in EP∩T-10∩F（S）. |
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| Keywords: | Banach spaces generalized equilibrium problem shrinking projection method quasi-φ-asymptotically nonexpansive mapping maximal monotone operator iterative sequence |
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