Strong convergence of monotone hybrid method for maximal monotone operators and hemirelatively nonexpansive mappings

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. Copyright © 2009 C. Klin-eam and S. Suantai.