Abstract
The present paper is devoted to the study of the generalized projection
π
K
:
X
∗
→
K
, where
X
is a uniformly convex and uniformly smooth Banach space and
K
is a nonempty closed (not necessarily convex) set in
X
. Our main result is the density of the points
x
∗
∈
X
∗
having unique generalized projection over nonempty close sets in
X
. Some minimisation principles are also established. An application to variational problems with nonconvex sets is presented.