Extensions and fixed points of contractive maps in Rn

Abstract This paper, which is written within the framework of Bishop's constructive mathematics, deals with the construction of the fixed point ξ of a contractive self-map f of R n, and with the rate at which the sequence (fn(x)) converges to ξ for any x in R n. It also discusses contractive extensions of contractive mappings on compact subsets of R n, and almost uniform contractions of complete metric spaces.