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.