Journal of Inequalities and Applications
Volume 2010 (2010), Article ID 251761, 16 pages
Research Article

A New Iteration Method for Nonexpansive Mappings and Monotone Mappings in Hilbert Spaces

Department of Mathematics, Dong-A University, Busan 604-714, South Korea

Received 5 October 2009; Accepted 20 December 2009

Academic Editor: Jong Kim

Copyright © 2010 Jong Soo Jung. 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.


We introduce a new composite iterative scheme by the viscosity approximation method for nonexpansive mappings and monotone mappings in a Hilbert space. It is proved that the sequence generated by the iterative scheme converges strongly to a common point of set of fixed points of nonexpansive mapping and the set of solutions of variational inequality for an inverse-strongly monotone mappings, which is a solution of a certain variational inequality. Our results substantially develop and improve the corresponding results of [Chen et al. 2007 and Iiduka and Takahashi 2005]. Essentially a new approach for finding the fixed points of nonexpansive mappings and solutions of variational inequalities for monotone mappings is provided.