Approximation of Fixed Points of Nonexpansive Mappings and Solutions of Variational Inequalities

Approximation of Fixed Points of Nonexpansive Mappings and Solutions of Variational Inequalities

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Abstract Let be a real Party Games -uniformly smooth Banach space with constant ,.Let and be a nonexpansive map and an -strongly accretive map which is also -Lipschitzian, respectively.Let be a real sequence in that satisfies the following condition: and.For and , define a sequence iteratively in by , ,.

Then, converges strongly to the unique solution of the variational inequality problem (search for such that here for all , where.A convergence theorem related to finite family of nonexpansive maps is also proved.