Strong convergence of an iterative procedure for pseudomonotone variational inequalities and fixed point problems

Abstract

Pseudomonotone variational inequalities have been investigated by
many authors, a common assumption ``weak sequential continuity"
being  imposed on pseudomonotone operators. In this paper, we
propose an iterative procedure for solving pseudomonotone
variational inequalities and fixed point problems of asymptotically
pseudocontractive operators by using self-adaptive techniques. Under
a weaker assumption than weak sequential continuity imposed on
pseudomonotone operators, we prove that the suggested procedure has
strong convergence.