| 强向量均衡问题与不动点问题的粘性逼近算法 |
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| 引用本文： | 李秋英,王三华.强向量均衡问题与不动点问题的粘性逼近算法[J].应用泛函分析学报,2012(2):183-192. |
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| 作者姓名： | 李秋英 王三华 |
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| 作者单位： | 南昌大学科技学院;南昌大学数学系 |
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| 基金项目： | 国家自然科学基金(11061023,11071108);江西省自然科学基金(2010GZS0145,2010GZS0151);江西省教育厅青年科学基金(GJJ10086);南昌大学科技学院基金(ZL-2010-01) |
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| 摘 要： | 讨论了强向量均衡问题与非扩张映射不动点问题的公共解.首先,给出了强向量均衡问题的辅助问题,并在适当的条件下,证明了其解的存在性和唯一性结果.然后,利用这些结果,提出了强向量均衡问题与非扩张映射不动点问题公共解的粘性逼近算法,并进一步证明了,在适当的条件下,由该算法产生的迭代序列强收敛于强向量均衡问题和非扩张映射不动点问题的公共解.
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| 关 键 词： | 强向量均衡问题 不动点问题 辅助问题 粘性逼近算法 强收敛 |
Viscosity Approximation Methods for Strong Vector Equilibrium Problems and Fixed Point Problems |
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| LI Qiuying,WANG Sanhua.Viscosity Approximation Methods for Strong Vector Equilibrium Problems and Fixed Point Problems[J].Acta Analysis Functionalis Applicata,2012(2):183-192. |
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| Authors: | LI Qiuying WANG Sanhua |
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| Institution: | 1.College of Science and Technology,Nanchang University,Nanchang 330029,China 2.Department of Mathematics,Nanchang University,Nanchang 330031,China |
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| Abstract: | In this paper,we study the problem of finding a common element of the set of solutions of a strong vector equilibrium problem and the set of fixed points of a nonexpansive mapping in Hilbert space.We first give the auxiliary problem for the strong vector equilibrium problem and obtain some results of existence and uniqueness of solutions of the auxiliary problem under suitable conditions.Then,by virtue of these results,we propose a viscosity iterative scheme for finding a common element of the set of solutions of the strong vector equilibrium problem and the set of fixed points of the nonexpansive mapping.Furthermore,we prove that,under suitable conditions,the sequences generated by this iterative scheme converge strongly to a common element of the set of solutions of the strong vector equilibrium problem and the set of fixed points of the nonexpansive mapping. |
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| Keywords: | strong vector equilibrium problem fixed point problem auxiliary problem viscosity approximation method strong convergence |
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