General iterative algorithms for monotone inclusion, variational inequality and fixed point problems

In this paper, we introduce two general iterative algorithms (one implicit algorithm and one explicit algorithm) for finding a common element of the solution set of the variational inequality problems for a continuous monotone mapping, the zero point set of a set-valued maximal monotone operator, and the fixed point set of a continuous pseudocontractive mapping in a Hilbert space. Then we establish strong convergence of the proposed iterative algorithms 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.