Accession Number : AD0761870

Title :   The Contraction Mapping Fixed Point Theorem in Interval Analysis.

Descriptive Note : Technical summary rept.,

Corporate Author : WISCONSIN UNIV MADISON MATHEMATICS RESEARCH CENTER

Personal Author(s) : Nickel,K. L.

Report Date : MAY 1973

Pagination or Media Count : 29

Abstract : 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)

Descriptors :   (*FUNCTIONAL ANALYSIS, THEOREMS), (*NUMERICAL ANALYSIS, THEOREMS), MAPPING(TRANSFORMATIONS), SET THEORY, APPROXIMATION(MATHEMATICS), COMPUTER PROGRAMMING

Subject Categories : Theoretical Mathematics

Distribution Statement : APPROVED FOR PUBLIC RELEASE