In this
paper, we study the regularization methods to approximate the solutions of the
variational inequalities with monotone hemi-continuous operator having
perturbed operators arbitrary. Detail, we shall study regularization methods to
approximate solutions of following variational inequalities:？and？with operator Abeing monotone hemi-continuous form real Banach reflexive X into its dual space X*,
but instead of knowing the exact data (y0, A), we only know its approximate data ？satisfying
certain specified conditions and D is
a nonempty convex closed subset of X;
the real function f defined on X is assumed to be lower
semi-continuous, convex and is not identical to infinity. At the same time, we
will evaluate the convergence rate of the approximate solution. The
regularization methods here are different from the previous ones.
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