Convergence theorem for I -asymptotically quasi-nonexpansive mapping in Hilbert space

Let H be a Hilbert space with inner product (·,·) and · norm, and let K be weakly compact a subset of H. Let T :K →K be nonlinear mapping and I :K →K be a nonlinear bounded mapping. In this paper, we define the I -asymptotically quasi-nonexpansive mapping in Hilbert space. If T is an I -asymptotically quasi-nonexpansive mapping, then we prove that 1 n n−1 i=0 T iu, for u ∈ K as n→∞, is weakly almost convergent to its asymptotic center. © 2006 Elsevier Inc. All rights reserved.