A general composite iterative algorithm for monotone mappings and pseudocontractive mappings in Hilbert spaces

Abstract

In this paper, we introduce a general composite iterative algorithm for finding a common element of the set of solutions of variational inequality problem for a hemicontinuous monotone mapping and the set of fixed points of a hemicontinuous pseudocontractive mapping in a Hilbert space. Under suitable control conditions, we establish strong convergence of the sequence generated by the proposed iterative algorithm to a common element of two sets, which is the unique solution of a certain variational inequality related to a boundedly Lipschitzian and strongly monotone mapping. As a consequence, we obtain the unique minimum-norm common point of two sets.