Copyright © 2009 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 propose a new viscosity iterative scheme for finding fixed points of nonexpansive mappings
in a reflexive Banach space having a uniformly Gâteaux differentiable norm and satisfying that every weakly compact convex subset of the space has the fixed point property for nonexpansive mappings. Certain different control conditions for viscosity iterative scheme are given and strong convergence of viscosity iterative
scheme to a solution of a ceratin variational inequality is established.