Journal of Applied Mathematics and Stochastic Analysis
Volume 2006 (2006), Article ID 21961, 13 pages
Approximating fixed points of non-self asymptotically nonexpansive
mappings in Banach spaces
Department of Mathematics, Tianjin Polytechnic University, Tianjin 300160, China
Received 23 March 2006; Revised 9 June 2006; Accepted 10 July 2006
Copyright © 2006 Yongfu Su and Xiaolong Qin. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
Suppose is a nonempty closed convex nonexpansive retract of a
real uniformly convex Banach space with as a nonexpansive
retraction. Let be an asymptotically
nonexpansive mapping with such that
and is nonempty, where
denotes the fixed points set of . Let , , and
be real sequences in (0,1) and
and some . Starting from arbitrary , define the sequence by , , , . (i) If the dual of has the Kadec-Klee property, then converges
weakly to a fixed point ; (ii) if satisfies condition (A), then converges strongly to a fixed point .