International Journal of Mathematics and Mathematical Sciences
Volume 2006 (2006), Article ID 46561, 6 pages

Approximation of fixed points of strongly pseudocontractive mappings in uniformly smooth Banach spaces

Xue Zhiqun

Department of Mathematics, Shijiazhuang Railway College, Shijiazhuang 050043, China

Received 3 March 2005; Revised 21 March 2006; Accepted 4 April 2006

Copyright © 2006 Xue Zhiqun. 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.


Let E be a real uniformly smooth Banach space, and K a nonempty closed convex subset of E. Assume that T1+T2: KK is a continuous and strongly pseudocontractive mapping, where T1:KK is Lipschitz and T2:KK has the bounded range mapping. Then the Ishikawa iterative sequence converges strongly to the unique fixed point of T1+T2.