zbMATH — the first resource for mathematics

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.

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
Full Text: DOI