| 高改良,周海云.Banach空间中一类K正定算子方程的可解性及其迭代构造[J].数学研究及应用,2004,24(1):149~154 |
| Banach空间中一类K正定算子方程的可解性及其迭代构造 |
| Solvability and Iterative Construction of Solution for a Class of K -Positive Definite Operator Equations in Banach Spaces |
| 投稿时间：2001-08-31 |
| DOI：10.3770/j.issn:1000-341X.2004.01.024 |
| 中文关键词: K-正定算子 可闭算子 可解性 迭代构造 |
| 英文关键词:K-positive definite operator closeable operator solvability iterative construction. |
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| 中文摘要: |
| 设X为Banach空间,A:D(A)?X→X为可闭的K一正定算子满足D(A)=D(K),则存在常数β>0,?x∈D(A),‖Ax‖≤β‖Kx‖,而且方程Ax=f(?f∈x)有唯一解.设{cn}n≥0为[0,1] 中实数列,定义迭代序列{xn}n≥0 如下:(?),则{xn}n≥0强收敛于方程Ax=f的唯一解. |
| 英文摘要: |
| Let X be a Banach space, and A:D(A)?X→X a closcable and K-positive definite operator with D(A) = D(K) . Then there exists a constant β>0 such that for any x∈D(A), || Ax ||≤β||Kx|| . Furthermore, the operator A is closed, R(A)=X, and the equation Ax=f, for any f∈X, has a unique solution. Let {cn}n≥0 be a real sequence in [0,1], Define the sequence {xn}n≥0 iteratively by ( I ) xn+1 = xn+ cnyn,yn=K-1f-K-1Axn, with x0∈D(A) . It is proved that the scquence ( I ) converges strongly to the unique solution of the equationin Ax=f in X. |
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