Copyright © 2012 Ruchi Das and Tarun Das. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

We define and study the notions of positively and negatively -asymptotic points for a homeomorphism on a metric -space. We obtain necessary and sufficient conditions for two points to be positively/negatively -asymptotic. Also, we show that the problem of studying -expansive homeomorphisms on a bounded subset of a normed linear -space is equivalent to the problem of studying linear -expansive homeomorphisms on a bounded subset of another normed linear -space.