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Zbl 0813.49010
Yao, Jen-Chih
Variational inequalities with generalized monotone operators.
(English)
[J] Math. Oper. Res. 19, No.3, 691-705 (1994). ISSN 1526-5471; ISSN 0364-765X/e

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.
[H.Benker (Merseburg)]
MSC 2000:
*49J40 Variational methods including variational inequalities
90C48 Programming in abstract spaces
90C33 Complementarity problems
49J27 Optimal control problems in abstract spaces (existence)

Keywords: variational inequalities; pseudomonotone operators; existence; uniqueness; minimization problems; pseudoconvex functions; Banach spaces

Cited in: Zbl 1020.47054

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