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 well-known 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