International Journal of Mathematics and Mathematical Sciences
Volume 2008 (2008), Article ID 649510, 9 pages
doi:10.1155/2008/649510

Strong convergence theorem of implicit iteration process for generalized asymptotically nonexpansive mappings in Hilbert space

Abstract

Let C be a nonempty closed and convex subset of a Hilbert space H, let T and S:C→C be two commutative generalized asymptotically nonexpansive mappings. We introduce an implicit iteration process of S and T defined by xn=αnx0+(1−αn)(2/((n+1)(n+2)))∑k=0n∑i+j=kSiTjxn, and then prove that {xn} converges strongly to a common fixed point of S and T. The results generalize and unify the corresponding results.