Copyright © 2010 Songnian He and Xiao-Lan Liang. 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.
Let be a real Hilbert space and let be a boundedly
Lipschitzian and strongly monotone operator. We design three hybrid steepest
descent algorithms for solving variational inequality of finding a point
such that ,
for all , where is the set of fixed
points of a strict pseudocontraction, or the set of common fixed points of finite
strict pseudocontractions. Strong convergence of the algorithms is proved.