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This article has been retracted as it is found to contain a substantial amount of material, without referencing, from the paper “On the Weak Relatively Nonexpansive Mappings in Banach Spaces,” Yongchun Xu and Yongfu Su, Fixed Point Theory and Applications, Volume 2010, Article ID 189751, 7 pages. doi:10.1155/2010/189751.

Abstract and Applied Analysis
Volume 2012, Article ID 730619, 7 pages
Review Article

On the Weak Relatively Nonexpansive Multivalued Mappings in Banach Spaces

Department of Mathematics, Tianjin Polytechnic University, Tianjin 300387, China

Received 12 July 2012; Accepted 7 August 2012

Academic Editor: Xiaolong Qin

Copyright © 2012 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.


In recent years, the definition of relatively nonexpansive multivalued mapping and the definition of weak relatively nonexpansive multivalued mapping have been presented and studied by many authors. In this paper, we give some results about weak relatively nonexpansive multivalued mappings and give two examples which are weak relatively nonexpansive multivalued mappings but not relatively nonexpansive multivalued mappings in Banach space 𝑙 2 and 𝐿 𝑝 [ 0 , 1 ] ( 1 < 𝑝 < + ∞ ) .