A THEOREM ON CONTRACTION MAPPINGS,
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)
Document Details
- Document Type
- Technical Report
- Publication Date
- Jan 01, 1969
- Accession Number
- AD0681577
Entities
People
- A. Meir
- Emmett Keeler
Organizations
- RAND Corporation