Original scientific paper
Maps for which some power is a contraction
Satish Shirali
; House No.899, Sector 21, Panchkula, Haryana, India
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.
Keywords
contraction; related metric; fixed point
Hrčak ID:
53215
URI
Publication date:
10.6.2010.
Visits: 1.652 *