Best Proximity Points for Alternative Maps.

Let (X, d) be a metric space and W i, i = 1, 2,..., m, be a nonempty subset of (X, d). An operator T : [1 i m W i ! [1 i m W i is called an alternative map if T (W j) [i 6= j W i, j = 1, 2,..., m. In addition, if for any x, y 2 [1 i m W i, there exists a constant a 2 [0, 1) such that d(Tx, Ty) ad(x, y) + (1 a)d(W j, W k) for some W j and W k 2 fW i g m i = 1 with x 2 W j and y 2 W k, then we call T an alternative contraction. Moreover, if (X, d) has an alternative UC property and T is an alternative contraction, then the best proximity point of T exists.