Fixed Point Theory and Applications
Volume 2009 (2009), Article ID 261932, 14 pages
doi:10.1155/2009/261932
Research Article

Strong Convergence of Monotone Hybrid Method for Maximal Monotone Operators and Hemirelatively Nonexpansive Mappings

Chakkrid Klin-eam and Suthep Suantai

Department of Mathematics, Faculty of Science, Chiang Mai University, Chiang Mai 50200, Thailand

Received 20 May 2009; Accepted 21 September 2009

Academic Editor: Wataru Takahashi

Copyright © 2009 Chakkrid Klin-eam and Suthep Suantai. 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

We prove strong convergence theorems for finding a common element of the zero point set of a maximal monotone operator and the fixed point set of a hemirelatively nonexpansive mapping in a Banach space by using monotone hybrid iteration method. By using these results, we obtain new convergence results for resolvents of maximal monotone operators and hemirelatively nonexpansive mappings in a Banach space.