Explicit Iteration Methods for Solving Variational Inequalities in Banach Spaces
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The problem of finding a solution of a variational inequality over the set of common fixed points of a nonexpansive semigroup is considered in a real and uniformly convex Banach space without imposing the sequential weak continuity of the normalized duality mapping. Two new explicit iterative methods are introduced based on the steepest-descent method, and conditions are given to obtain their strong convergence. A numerical example is showed to illustrate the convergence analysis of the proposed methods.
KeywordsVariational inequality Common fixed point Nonexpansive semigroup Accretive mapping Explicit method
Mathematics Subject Classification41A65 47H17 47H20
The authors are very grateful to the referees for their useful comments, which helped to improve the paper.
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