| Banach空间中有限个增生算子公共零点的迭代强收敛定理 |
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| 引用本文： | 魏利,谭瑞林,周海云. Banach空间中有限个增生算子公共零点的迭代强收敛定理[J]. 数学的实践与认识, 2009, 39(10) |
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| 作者姓名： | 魏利 谭瑞林 周海云 |
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| 作者单位： | 1. 河北经贸大学,数学与统计学学院,河北,石家庄,050061
2. 军械工程学院,应用数学与力学研究所,河北,石家庄,050003 |
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| 基金项目： | 国家自然科学基金，河北省教育厅自然科学研究项目 |
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| 摘 要： | 令E为实自反Banach空间具一致Gteaux可微范数,AiE×E(i=1,2,…,k)为增生算子且满足∩ki=1Ai-1(0)≠φ.令C为E的非空闭凸子集并满足■C∩r>0R(I+rAi),i=1,2,…,k.将引入一种带误差项的迭代算法,并证明迭代序列强收敛于{Ai}ki=1的公共零点.
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| 关 键 词： | 增生算子 保核收缩映射 非扩展映射 零点 |
Strong Iterative Convergence Theorem of Common Zero Points For Finite Accretive Operators in Banach Space |
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| WEI Li,TAN Rui-lin,ZHOU Hai-yun. Strong Iterative Convergence Theorem of Common Zero Points For Finite Accretive Operators in Banach Space[J]. Mathematics in Practice and Theory, 2009, 39(10) |
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| Authors: | WEI Li TAN Rui-lin ZHOU Hai-yun |
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| Abstract: | Let E be a real reflexive Banach space with uniformly Gteaux differential norm and AiE×E,i=1,2,…,k be accretive operators.Suppose that ∩ki=1A-1i(0)≠φ. Let CE be a nonempty closed convex set and satisfy that D(Ai)C∩r>0R(I+rAi), for i=1,2,…,k. A proximal iterative algorithm is introduced which is proved to be strongly convergent to common zero points of accretive operators {Ai}ki=1. |
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| Keywords: | Accretive operator retraction nonexpansive mapping zero point |
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