Fixed points of nonexpanding maps

Introduction. This paper is concerned with nonexpanding maps from the unit ball of a real Hubert space into itself. Browder [l] has established that such maps always possess at least one fixed point. We shall develop a method, which resembles the simple iterative method, for approximating fixed points of such maps. In fact, we shall generate a sequence, {x n }, by the recursive formula x n+ i = k n +if(xn) where is the map in question and {k n } is a sequence of real numbers. Our main result is Theorem 3 which states sufficient conditions on k n to insure the strong convergence of x n to a fixed point of .