NEAREST POINTS an‎d FARTHEST POINTS WITH APPLICATIONS

In this paper we show the best approximation and the set farthest points in normed spaces with intersections of unit balls. We nd interesting relationship between the nearest and the farthest points in normed linear spaces. Also we obtain a necessary and a sucient condition for the set of !0-nearest points ( !0- farthest points) to be non-empty or a singleton set in normed linear spaces. We nd a necessary and a sucient condition for a uniquely remotal set to be a singleton set.