Generalized projections on closed nonconvex sets in uniformly convex and uniformly smooth Banach spaces (Q490929)

Summary: The present paper is devoted to the study of the generalized projection \(\pi_K: X^{\ast}\to K\), 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 \(x^{\ast}\in X^{\ast}\) having unique generalized projection over nonempty closed sets in \(X\). Some minimisation principles are also established. An application to variational problems with nonconvex sets is presented.