VARIATIONAL-INEQUALITIES WITH GENERALIZED MONOTONE-OPERATORS

We investigate the variational inequality with pseudomonotone operator s (in the sense of Karamardian) in Banach spaces. New existence result s which extend many known results in infinite-dimensional spaces are d erived under rather weak assumptions. New uniqueness results which als o seem to be new even in finite-dimensional spaces are also derived. I n particular, new existence and uniqueness results for the complementa rity problem with pseudomonotone operators in Banach spaces are obtain ed. Also, existence and uniqueness results for minimization problems w ith pseudoconvex functions in Banach spaces are obtained.