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Variational Inequalities with Generalized Monotone Operators

We investigate the variational inequality with pseudomonotone operators in the sense of Karamardian in Banach spaces. New existence results which extend many known results in infinite-dimensional spaces are derived under rather weak assumptions. New uniqueness results which also seem to be new even in finite-dimensional spaces are also derived. In particular, new existence and uniqueness results for the complementarity problem with pseudomonotone operators in Banach spaces are obtained. Also, existence and uniqueness results for minimization problems with pseudoconvex functions in Banach spaces are obtained.