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.