Fixed Point Theory and Applications
Volume 2010 (2010), Article ID 189751, 7 pages
doi:10.1155/2010/189751
Research Article

On the Weak Relatively Nonexpansive Mappings in Banach Spaces

Yongchun Xu1 and Yongfu Su2

1Department of Mathematics, Hebei North University, Zhangjiakou 075000, China
2Department of Mathematics, Tianjin Polytechnic University, Tianjin 300160, China

Received 23 March 2010; Accepted 20 May 2010

Academic Editor: Billy Rhoades

Copyright © 2010 Yongchun Xu and Yongfu Su. 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.

Abstract

In recent years, the definition of weak relatively nonexpansive mapping has been presented and studied by many authors. In this paper, we give some results about weak relatively nonexpansive mappings and give two examples which are weak relatively nonexpansive mappings but not relatively nonexpansive mappings in Banach space l2 and Lp[0,1]   (1<p<+∞).