Maps for which some power is a contraction
Year: 2010
Type: article
Abstract: It is well known that if some power of a self map of a complete metric space is a contraction, then the map has a unique fixed point.It is natural to ask whether such a map is itself a contraction with respect to some related metric on the space.We show that this is indeed so and furthermore, if the map is uniformly continuous, then the related metric is complete.Also, we give an example to show that, if the map is not continuous, then the related metric need not be complete.
Author: Satish Shirali
Language: English
Subfield: Geometry and Topology
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W2188724535