some new results on remotest points in normed spaces

In this paper, using the best proximity theorems for an extension of brosowski's theorem. we obtain other results on farthest points. finally, we de ne the concept of є- farthest points. we shall prove interesting relationship between the є-best approximation and the є-farthest points in normed linear spaces (x; k:k). if z 2 w is a є-farthest point from an x 2 x, then z is also a є-best approximation in w.