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.