International Journal of Mathematics and Mathematical Sciences
Volume 2005 (2005), Issue 17, Pages 2711-2718

Iterative approximation of fixed point for Φ-hemicontractive mapping without Lipschitz assumption

Xue Zhiqun

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

Received 30 December 2004; Revised 7 July 2005

Copyright © 2005 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 an arbitrary real Banach space and let K be a nonempty closed convex subset of E such that K+KK. Assume that T:KK is a uniformly continuous and Φ-hemicontractive mapping. It is shown that the Ishikawa iterative sequence with errors converges strongly to the unique fixed point of T.