Abstract
We introduce an iterative process which converges strongly to a common fixed point of a finite family of uniformly continuous asymptotically k(i)-strict pseudocontractive mappings in the intermediate sense for i = 1, 2,...,N. The projection of x(0) onto the intersection of closed convex sets C-n and Q(n) for each n >= 1 is not required. Moreover, the restriction that the interior of common fixed points is nonempty is not required. Our theorems improve and unify most of the results that have been proved for this important class of nonlinear mappings.