| 扰动m-增生算子方程的Ishikawa迭代程序 |
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| 引用本文： | 沈自飞,杨敏波.扰动m-增生算子方程的Ishikawa迭代程序[J].数学学报,2005,48(4):801-808. |
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| 作者姓名： | 沈自飞 杨敏波 |
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| 作者单位： | [1]浙江师范大学数学系,金华321004／／北京信息控制研究所,北京100037 [2]浙江师范大学数学系,金华321004 |
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| 基金项目： | 国家自然科学基金资助项目(10471113)，浙江省自然科学基金资助项目(M103098) |
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| 摘 要： | 设X是光滑Banach空间,A:X→X是一致连续的m-增生算子,S:X→X是一致连续的φ--强增生算子,本文证明实光滑Banach空间上连续的m-增生算子是单值的且具误差的Ishikawa和Mann迭代序列强收敛到方程z=Sx+λAx的唯一解,其中z∈X,λ≥0.我们的结果改进和推广了近期文献中的相应结果.
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| 关 键 词： | m-增生算子 φ-强增生算子 Ishikawa和Mann迭代 |
Ishikawa Iterative Process with Errors for Perturbed m-Accretive Operator Equations |
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| Zi Fei SHEN.Ishikawa Iterative Process with Errors for Perturbed m-Accretive Operator Equations[J].Acta Mathematica Sinica,2005,48(4):801-808. |
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| Authors: | Zi Fei SHEN |
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| Institution: | Zi Fei SHEN Department of Mathematics, Zhejiang Normal University, Jinhua 321004, P. R. China Beijing Institute of Information and Control, Beijing 100037, P. R. China Min Bo YANG Department of Mathematics, Zhejiang Normal University, Jinhua 321004, P. R. China |
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| Abstract: | Let X be a smooth Banach space, A : X→X a uniformly continuous m-accretive operator, S: X→X a uniformly continuous φ-accretive operator. It is proved that a continuous m-accretive operator on a real smooth Banach space is single-valued and the Ishikawa and Mann iterative processes with errors converge strongly to the unique solution of the equation z=Sx+λAx for given z∈X and λ≥0. Our results improve and generalize some recent results in the literature greatly. |
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| Keywords: | m-accretive operator φ-accretive operator Ishikawa and Mann iterative processes |
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