On Kirk's asymptotic contractions |
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Authors: | Jacek Jachymski,Izabela Jó ?wik |
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Affiliation: | a Institute of Mathematics, Technical University of ?ód?, ?wirki 36, 90-924 ?ód?, Poland b Institute of Mathematics and Centre of Mathematics and Physics, Technical University of ?ód?, ?wirki 36, 90-924 ?ód?, Poland |
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Abstract: | 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. |
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Keywords: | Asymptotic fixed point theory Asymptotic contractions Contractive fixed point Approximate fixed point Separation theorem |
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