The Contraction Mapping Fixed Point Theorem in Interval Analysis

摘要

The fixed point equation X = F(X) 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 F(X). One of them is a constructive realization of the Brouwer fixed point theorem. For the other three cases F(X) has to be a contraction mapping. Numerical examples are discussed and a Triplex-ALGOL 60 computer program is given. (Author)