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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 \[ (x- \bar x, T\bar x)\geq 0\quad\text{for all } x\in K, \] where \(T\) is an operator from a closed convex subset \(K\) of \(B\) into \(B^*\), \(B\) is a real Banach space with norm \(\|.\|\), \(B^*\) is its topological conjugate space endowed with weak * topology and \((u,\nu)\) is the paring between \(u\in B^*\) and \(\nu\in B^*\). In a final section same existence and uniqueness results for minimization problems with pseudoconvex functions in Banach spaces are obtained.

MSC:
49J40 Variational inequalities
90C48 Programming in abstract spaces
90C33 Complementarity and equilibrium problems and variational inequalities (finite dimensions) (aspects of mathematical programming)
49J27 Existence theories for problems in abstract spaces
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