%0 Journal Article
%T A New Iteration Method for Nonexpansive Mappings and Monotone Mappings in Hilbert Spaces
%A Jong Soo Jung
%J Journal of Inequalities and Applications
%D 2010
%I Springer
%R 10.1155/2010/251761
%X 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.
%U http://dx.doi.org/10.1155/2010/251761