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Strong vector variational inequalities in Banach spaces. (English) Zbl 1138.49300
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)].

49J40Variational methods including variational inequalities
47H10Fixed-point theorems for nonlinear operators on topological linear spaces
47J20Inequalities involving nonlinear operators
Full Text: DOI
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