
Accession Number : AD0681577
Title : A THEOREM ON CONTRACTION MAPPINGS,
Corporate Author : RAND CORP SANTA MONICA CALIF
Personal Author(s) : Keeler,Emmett ; Meir,A.
Report Date : JAN 1969
Pagination or Media Count : 7
Abstract : In this note (X, rho) will be a complete metric space and f a mapping of X into itself. A wellknown theorem of Banach states: If there exists an alpha < 1 such that for all x, y epsilon X rho(f(x), f(y)) = or < alpha . rho (x,y), alpha < 1 then f has a unique fixpoint (i.e., point xi such that f (xi) = xi). It is shown that the conclusion of Banach's Theorem holds more generally from a condition of weakly uniformly strict contraction. (Author)
Descriptors : (*MAPPING(TRANSFORMATIONS), THEOREMS), TOPOLOGY
Subject Categories : Theoretical Mathematics
Distribution Statement : APPROVED FOR PUBLIC RELEASE