On Kirk's asymptotic contractions

[摘要] Recently Kirk introduced the notion of asymptotic contractions on a metric space and using ultrapower techniques he obtained an asymptotic version of the Boyd-Wong fixed point theorem. In this paper we extend this result and moreover, we give a constructive proof of it. Furthermore, we obtain a complete characterization of asymptotic contractions on a compact metric space. As a by-product we establish a separation theorem for upper semicontinuous functions satisfying some limit condition. (C) 2004 Elsevier Inc. All rights reserved.

[发布日期] 2004-12-01

[关键词] asymptotic fixed point theory;asymptotic contractions;contractive fixed point;approximate fixed point;separation theorem