Department of Mathematics, Graduate School of Environment and Information Sciences, Yokohama National University, Tokiwadai, Hodogayaku, Yokohama 240-8501, Japan
Academic Editor: S. Reich
Copyright © 2010 Hiroko Manaka. 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 a smooth Banach space with a norm . Let for any , where stands for the duality
pair and J is the normalized duality mapping. With respect to this bifunction
, a generalized nonexpansive mapping and a -strongly nonexpansive
mapping are defined in . In this paper, using the properties of generalized
nonexpansive mappings, we prove convergence theorems for common zero
points of a maximal monotone operator and a -strongly nonexpansive mapping.