Abstract
It is shown that if a mapping is a local radial contraction defined on a metric space
(
X
,
d
)
which takes values in a metric transform of
(
X
,
d
)
, then for many metric transforms it is also a local radial contraction (with possibly different contraction constant) relative to the original metric. Several specific examples are given. This in turn implies that the mapping has a fixed point if the space is rectifiably pathwise connected. Some results about set-valued contractions are also discussed.