Fixed Point Theory and Applications
Volume 2010 (2010), Article ID 512751, 15 pages
Research Article

Existence of Fixed Points of Firmly Nonexpansive-Like Mappings in Banach Spaces

1Department of Economics, Chiba University, Yayoi-cho, Inage-ku, Chiba-shi, Chiba 263-8522, Japan
2Department of Computer Science and Intelligent Systems, Oita University, Dannoharu, Oita-shi, Oita 870-1192, Japan

Received 27 November 2009; Accepted 12 February 2010

Academic Editor: Tomonari Suzuki

Copyright © 2010 Koji Aoyama and Fumiaki Kohsaka. 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.


The aim of this paper is to obtain some existence theorems related to a hybrid projection method and a hybrid shrinking projection method for firmly nonexpansive-like mappings (mappings of type (P)) in a Banach space. The class of mappings of type (P) contains the classes of resolvents of maximal monotone operators in Banach spaces and firmly nonexpansive mappings in Hilbert spaces.