On a general nonlinear variational inequality

Abstract

Variational inequality theory provides techniques for solving a variety of applied problems in science and engineering. Recently Noor considered some interesting general nonlinear and linear variational inequalities in a series of papers and proved the existence and uniqueness of solutions by a fixed point technique developed by Glowinski, Lions and Tremolieres and also by a fixed point technique of Lions and Stampacchia. But there are several inaccuracies in his proofs and here they have been removed and correct formulation of the theorems are stated and proved and relationships are clearly shown. The existence of solution necessitates an additional condition in one case, and less condition in the other, but uniqueness can be proved without the condition that the operator be antimonotone.