Abstract
In this paper, in order to solve a variational inequality problem over the fixed point set of a nonexpansive mapping on uniformly smooth or reflexive and strictly convex Banach spaces with a uniformly Gâteaux differentiable norm, we investigate an explicit iteration method, based on the steepest-descent and Krasnosel’skii–Mann algorithms. We also show that some modifications of the last and Halpern-type algorithms are special cases of our result.
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