The Contraction Mapping Fixed Point Theorem in Interval Analysis.
Technical summary rept.,
WISCONSIN UNIV MADISON MATHEMATICS RESEARCH CENTER
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The fixed point equation X FX is considered in the set R of all real finite intervals. Despite the fact that R is not a linear space the contraction mapping fixed point theorem can be used in R. In the paper, four theorems give constructive ways of computing a fixed interval for a given function FX. One of them is a constructive realization of the Brouwer fixed point theorem. For the other three cases FX has to be a contraction mapping. Numerical examples are discussed and a Triplex-ALGOL 60 computer program is given. Author
- Theoretical Mathematics