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Zbl 1138.49300
Fang, Ya-Ping; Huang, Nan-Jing
Strong vector variational inequalities in Banach spaces.
(English)
[J] Appl. Math. Lett. 19, No. 4, 362-368 (2006). ISSN 0893-9659

Summary: In this work, we study some existence results for solutions for a class of strong vector variational inequalities (for short, SVVI) in Banach spaces. The solvability of the $SVVI$ without monotonicity is presented by using the fixed point theorems of Brouwer and Browder, respectively. The solvability of the SVVI with monotonicity is also proved by using the {\it Ky Fan} lemma [Math. Ann. 266, No. 4, 519--537 (1984; Zbl 0515.47029)]. Our results give a positive answer to an open problem proposed by {\it G. Chen} and {\it S.-H. Hou} [Nonconvex Optim. Appl. 38, 73--86 (2000; Zbl 1012.49007)].
MSC 2000:
*49J40 Variational methods including variational inequalities
47H10 Fixed point theorems for nonlinear operators on topol.linear spaces
47J20 Inequalities involving nonlinear operators

Keywords: strong vector variational inequality; Brouwer's fixed point theorem; weak coercivity; pseudomonotone mapping; solvability

Citations: Zbl 0515.47029; Zbl 1012.49007

Cited in: Zbl 1178.49014 Zbl 1129.49008

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