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Viscosity iterations which include contraction mapping have been widely used to find solutions of equilibrium problems. Here we introduce a modification of the viscosity iteration scheme by replacing the contraction with a weak contraction. Weakly contractive mappings are intermediate to contractive and nonexpansive mappings and are known to have unique fixed points in complete metric spaces. We apply this iteration to the case of a generalized equilibrium problem. The special case where the weak contraction is a contraction has also been discussed. c ©2012 NGA. All rights reserved.

A viscosity type iteration by weak contraction for approximating solutions of generalized equilibrium problem