In this paper, we introduce three new iteration methods, which
are implicit and converge strongly, based on the steepest descent method with
a strongly accretive and strictly pseudocontractive mapping and the modied
Halpern's iterative scheme, for nding a solution of variational inequalities
over the set of common xed points of a nonexpansive semigroup on a real
Banach space which has a uniformly G^ateaux dierentiable norm.

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