Abstract
In this paper, for a commuting pair consisting of a point-valued nonexpansive self-mapping
t and a set-valued nonexpansive self-mapping
T of a hyperconvex metric space (or a CAT(0) space)
X, we look for a solution to the problem of existence of
z
∈
E
⊂
X
such that
d
(
z
,
y
)
=
d
(
y
,
E
)
and
z
=
t
(
z
)
∈
T
(
z
)
.