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Abstract and Applied Analysis
Volume 2012 (2012), Article ID 237820, 10 pages
http://dx.doi.org/10.1155/2012/237820
Research Article

Asymptotic Properties of -Expansive Homeomorphisms on a Metric -Space

Department of Mathematics, Faculty of Science, The M. S. University of Baroda, Vadodara 390002, India

Received 21 August 2012; Accepted 27 September 2012

Academic Editor: Ngai-Ching Wong

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.