CONVERGENCE OF SOME ITERATIVE METHODS FOR MONOTONE INCLUSION, VARIATIONAL INEQUALITY AND FIXED POINT PROBLEMS (Study on Nonlinear Analysis and Convex Analysis)

Abstract

In this paper, we introduce two iterative methods (one implicit method and one explicit method) for finding a common element of the zero point set of a set-valued maximal monotone operator, the solution set of the variational inequality problem for a continuous monotone mapping, and the fixed point set of a continuous pseudocontractive mapping in a Hilbert space. Then we establish strong convergence of the proposed iterative methods 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. The main theorems develop and complement some well-known results in the literature.