Mathematics and Text

Let H be a Hilbert space, C be a closed bounded convex subset of H, T a nonexpansive self map of C. Suppose that as n→∞, an, k→ 0 for each k, and γn = $\sum_{{k=0}}^{{\infty }}$$\left(\vphantom{ a_{n,k+1}-a_{n,k}}\right.$an, k+1 - an, k$\left.\vphantom{ a_{n,k+1}-a_{n,k}}\right)^{{+}}_{}$→ 0 Then for each x in C, Anx = $\sum_{{k=0}}^{{\infty }}$an, kTkx converges weakly to a fixed point of T .