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.