International Journal of Mathematics and Mathematical Sciences
Volume 2005 (2005), Issue 11, Pages 1685-1692
doi:10.1155/IJMMS.2005.1685

Fixed point iteration for asymptotically quasi-nonexpansive mappings in Banach spaces

Abstract

Suppose that C is a nonempty closed convex subset of a real uniformly convex Banach space X. Let T:C→C be an asymptotically quasi-nonexpansive mapping. In this paper, we introduce the three-step iterative scheme for such map with error members. Moreover, we prove that if T is uniformly L-Lipschitzian and completely continuous, then the iterative scheme converges strongly to some fixed point of T.