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We introduce a new iterative algorithm for finding a common element of the solution set of the variational inequality problem for a continuous monotone mapping, the zero point set of a maximal monotone operator, and the fixed point set of a continuous pseudocontractive mapping in a Hilbert space. Then we establish strong convergence of the sequence generated by the proposed algorithm to a common point of three sets, which is a solution of a certain variational inequality. Further, we find the minimum-norm element in common set of three sets. As applications, we consider iterative algorithms for the equilibrium problem coupled with fixed point problem. ©2016 All rights reserved.

Strong convergence theorems for maximal monotone operators and continuous pseudocontractive mappings