| 葛人溥.算子的旋转度及其在研究算子不动点中的应用[J].数学研究及应用,1982,2(1):29~36 |
| 算子的旋转度及其在研究算子不动点中的应用 |
| The Rotation Degree of an Operator and its Applications to the Research of Finding Fixed Points of Operators |
| 投稿时间：1981-05-21 |
| DOI：10.3770/j.issn:1000-341X.1982.01.007 |
| 中文关键词: |
| 英文关键词: |
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| 中文摘要: |
| 在研究算子不动点的过程中,人们早已注意到算子的相对伸长度在证明其不动点存在唯一性以及寻找不动点中的作用。但是从六十年代末开始,人们注意到这样的事实:决定算子不动点的存在唯一性及寻找方法的不仅仅是伸长度,它还与内积有关。这就导致了对所谓单调算子与伪压缩算子的研究。上以f表示实Hilbert空间中的算子,x,y是空间中的元素。本文认为实Hilbert空间中的算子的作用实际上是由两部分组成的:旋转与伸长,并利用旋转度与伸长度的概念研究了一类非膨胀算子以及一类可膨胀算子的不动点的存在唯一性以及寻找它们的一种迭代方法。最后,我们还发现了均匀膨胀算子存在唯一不动点的条件,并给出了寻找这种不动点的反代法。 |
| 英文摘要: |
| In the research on the existence and uniqueness of fixed points of operators as well as the method for finding them, the action of the relative lengthened degree was noticed about seventy years ago. From the end of the sixties on, it is noticed that the determination of the existence and uniqueness of fixed points of operators as well as the method for finding them is related for not only the lengthened degree but also the inner product. The latter caused the research on monotonic operators and pseudo-constract operators. Here f expresses an operator in a real Hilbert space and x, y are elements of this space. In this article we find out that the action of an operator in areal Hilbert space in fact cohsists of two parts: rotating and lengthening. We use the concepts of the 1otationdegree and lengthened degree to research the existence and uniqueness of fixed point
of points operator, which belongs to a class of nonexpansive operators and of aclass of expansible operators and to give the iterative methods for finding it. |
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