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Variational inequalities with generalized monotone operators. (English) Zbl 0813.49010
The purpose of this paper is to derive some more existence results for pseudomonotone operators $T$ for the problem: Find $\bar x\in K$ such that $$(x- \bar x, T\bar x)\ge 0\quad\text{for all } x\in K,$$ where $T$ is an operator from a closed convex subset $K$ of $B$ into $B\sp*$, $B$ is a real Banach space with norm $\Vert.\Vert$, $B\sp*$ is its topological conjugate space endowed with weak * topology and $(u,\nu)$ is the paring between $u\in B\sp*$ and $\nu\in B\sp*$. In a final section same existence and uniqueness results for minimization problems with pseudoconvex functions in Banach spaces are obtained.

49J40Variational methods including variational inequalities
90C48Programming in abstract spaces
90C33Complementarity and equilibrium problems; variational inequalities (finite dimensions)
49J27Optimal control problems in abstract spaces (existence)
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