Abstract and Applied Analysis

Asymptotic Properties of $G$-Expansive Homeomorphisms on a Metric $G$-Space

Abstract

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

Article information

Source
Abstr. Appl. Anal., Volume 2012 (2012), Article ID 237820, 10 pages.

Dates
First available in Project Euclid: 28 March 2013

Permanent link to this document
https://projecteuclid.org/euclid.aaa/1364475909

Digital Object Identifier
doi:10.1155/2012/237820

Mathematical Reviews number (MathSciNet)
MR2994931

Zentralblatt MATH identifier
1262.54012

Citation

Das, Ruchi; Das, Tarun. Asymptotic Properties of $G$ -Expansive Homeomorphisms on a Metric $G$ -Space. Abstr. Appl. Anal. 2012 (2012), Article ID 237820, 10 pages. doi:10.1155/2012/237820. https://projecteuclid.org/euclid.aaa/1364475909

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