Bulletin of the Australian Mathematical Society

Research Article

Strong Convergence of Approximating Fixed Point Sequences for Nonexpansive Mappings

Hong-Kun Xua1

a1 School of Mathematical Sciences University of KwaZulu-Natal Westville Campus Private Bag X54001 Durban 4000 South Africa e-mail: xuhk@ukzn.ac.za

Consider a nonexpansive self-mapping T of a bounded closed convex subset of a Banach space. Banach's contraction principle guarantees the existence of approximating fixed point sequences for T. However such sequences may not be strongly convergent, in general, even in a Hilbert space. It is shown in this paper that in a real smooth and uniformly convex Banach space, appropriately constructed approximating fixed point sequences can be strongly convergent.

(Received April 26 2006)