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Journal of Function Spaces
Volume 2015, Article ID 478437, 7 pages
http://dx.doi.org/10.1155/2015/478437
Research Article

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

Department of Mathematics, College of Science, King Saud University, P.O. Box 2455, Riyadh 11451, Saudi Arabia

Received 6 April 2015; Accepted 30 May 2015

Academic Editor: Calogero Vetro

Copyright © 2015 Messaoud Bounkhel. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

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