Fixed point theorems by altering distances between the points 1

1. cp is continuous and strictly increasing in R ; 2. ip(t) = 0 if and only if t = 0 ; 3. 0 , where M > 0 , \i > 0 are constant. We denote the set of above functions ip with $ . Precisely in [S, corol. 2] the following theorem was proved: THEOREM 1. Let T be a selfmap of a complete metric space (X,d) and tp £ $ such that for every x,y in X, (A) w(d(Tx,Ty)) < a.y(d(x,y)) + b.y$>(d(x,Tx))