The Rotation Degree of an Operator and its Applications to the Research of Finding Fixed Points of Operators |
Received:May 21, 1981 |
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Abstract: |
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. |
Citation: |
DOI:10.3770/j.issn:1000-341X.1982.01.007 |
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