A new explicit iteration method for variational inequalities on the set of common fixed points for a finite family of nonexpansive mappings

摘要

In this paper, we introduce a new explicit iteration method based on the steepest descent method and Krasnoselskii-Mann type method for finding a solution of a variational inequality involving a Lipschitz continuous and strongly monotone mapping on the set of common fixed points for a finite family of nonexpansive mappings in a real Hilbert space. MSC:41A65, 47H17, 47H20.