Generalized Projections on Closed Nonconvex Sets in Uniformly Convex and Uniformly Smooth Banach Spaces

الملخص EN

The present paper is devoted to the study of the generalized projection πK: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.